Engineering Mechanics Exercise on Projectile Motion (Unit-III) 1 A projectile is fired with velocity 620 m/s at an angle of 40 with horizontal ground. Find the range, time of flight, maximum height attained by projectile and the velocity just before striking the ground. 2 A projectile is fired from a edge of 150 m cliff with an initial velocity of 180 m/s at an angle of 30 degree with horizontal. Neglecting air resistance determines (a) Horizontal distance from the gun to the point where projectile strikes ground (b) the greatest elevation above the ground reached by the projectile. 3 A projectile is fired with an initial velocity of 244 m/s at target B located 610 m above the gun A and horizontal distance of 3658 m. determine value of firing angle 4 A tennis player serves the ball at a height h with an initial velocity of 40 m/s at an angle of 4 with the horizontal. Knowing that the ball clears the 0.914 m net by 152 mm, determine (a) the height h, (b) the distance d from the net to where the ball will land. 5 A golfer hits a ball with an initial velocity of magnitude v 0 at an angle α with the horizontal. Knowing that the ball must clear the tops of two trees and land as close as possible to the flag, determine v 0 and the distance d when the golfer uses (a) a six-iron with α = 31, (b) a five-iron with α = 27. 6 A ski jumper starts with a horizontal take-off velocity of 25 m/s and lands on a straight landing hill inclined at 30o. Determine (a) the time between take-off and landing, (b) the length d of the jump. 7 8 A bullet is fired from horizontal distance of 44m measured from bottom of a 12 m high vertical pole. Calculate velocity of projection such that bullet can just clear the upper end of the pole A shot is fired at an elevation of 60 degree with velocity of 60 m/s. State the position of the shot at 2 sec after firing. What will be velocity at that instant? 9 A homeowner uses a snow blower to clear his driveway. Knowing that the snow is discharged at an average angle of 40 with the horizontal, determine the initial speed v0 of the snow.
10 A golfer aims his shot to clear the top of a tree by a distance h at the peak of the trajectory and to miss the pond on the opposite side. Knowing that the magnitude of v0 is 30 m/s, determine the range of values of h which must be avoided. 11 A handball player throws a ball from A with a horizontal velocity v0. Knowing that d = 15 ft, determine (a) the value of v0 for which the ball will strike the corner C, (b) the range of values of v0 for which the ball will strike the corner region BCD. 12 A helicopter is flying with a constant horizontal velocity of 90 mi/h (144.2 kmph) and is directly above point A when a loose part begins to fall. The part lands 6.5 s later at point B on an inclined surface. Determine (a) the distance d between points A and B, (b) the initial height h. 14 A basketball player shoots when she is 5 m from the backboard. Knowing that the ball has an initial velocity v 0 at an angle of 30 with the horizontal, determine the value of v 0 when d is equal to (a) 228 mm, (b) 430 mm. 15 A ball is projected from point A with a velocity v 0 which is perpendicular to the incline shown. Knowing that the ball strikes the incline at B, determine the initial speed v 0 in terms of the range R and β. 16 An outfielder throws a ball with an initial velocity of magnitude v 0 at an angle of 10 with the horizontal to the catcher 50 m away. Knowing that the ball is to arrive at a height between 0.5 m and 1.5 m, determine (a) the range of values of v 0, (b) the range of values of the maximum height h of the trajectory.
17 A model rocket is launched from point A with an initial velocity v 0 of 86 m/s. If the rocket s descent parachute does not deploy and the rocket lands 104 m from A, determine (a) the angle α that v 0 forms with the vertical, (b) the maximum height h reached by the rocket, (c) the duration of the flight. 18 The initial velocity v0 of a hockey puck is 170 km/h. Determine (a) the largest value (less than 45 ) of the angle α for which the puck will enter the net, (b) the corresponding time required for the puck to reach the net. 19 A projectile is launched from point A with an initial velocity v 0 of 120 ft/s at an angle α with the vertical. Determine (a) the distance d to the farthest point B on the hill that the projectile can reach, (b) the corresponding angle α, (c) the maximum height of the projectile above the surface. 20 A sack slides off the ramp, shown in Fig. with a horizontal velocity of 12 m/s. If the height of the ramp is 6 m from the floor, determine the time needed for the sack to strike the floor and the range R where sacks begin to pile up. 21 The chipping machine is designed to eject wood chips at v 0 = 25 ft/s as shown in Fig. If the tube is oriented at 30 from the horizontal, determine how high, h, the chips strike the pile if at this instant they land on the pile 20 ft from the tube. 22 The ball is kicked from point A with the initial velocity 10 m/s. Determine the maximum height h it reaches. Also Determine the range R, and the speed when the ball strikes the ground.
23 Determine the speed at which the basketball at A must be thrown at the angle of 30 so that it makes it to the basket at B. 24 Water is sprayed at an angle of 90 from the slope at 20 m/s. Determine the range R. 25 A ball is thrown from A. If it is required to clear the wall at B, determine the minimum magnitude of its initial velocity. 26 A projectile is fired with an initial velocity of 150 m/s off the roof of the building. Determine the range R where it strikes the ground at B. 27 The ball i s thrown off the top o f the building. If it strikes the ground at B in 3 s, determine the initial velocity and the inclination angle ( ) A at which it was thrown. Also, find the magnitude of the ball's velocity when it strikes the ground. 28 The fireman holds the hose at an angle ( ) = 30 with horizontal, and the water is discharged from the hose at A with a speed of v A = 40 ft/s. If the water stream strikes the building at B, determine his two possible distances s from the building.
29 A projectile is fired with a speed of v = 60 m/s at an angle of 60. A second projectile is then fired with the same speed 0.5 s later. Determine the angle ( ) of the second projectile so that the two projectiles collide. At what position (x, y) will this happen? 30 Water is discharged from the hose with a speed of 40 ft/s. Determine the two possible angles ( ) the fireman can hold the hose so that the water strikes the building at B. Take s = 20 ft. 31 It is observed that the time for the ball to strike the ground at B is 2.5 s. Determine the speed V A and angle A at which the ball was thrown. 32 The golf ball is hit a t A with a speed o f VA = 40 m/s and directed at an angle of 30 with the horizontal as shown. Determine the distance d where the ball strikes the slope at B. 33 If the football is kicked at the 45 angle, determine its minimum initial speed V A so that it passes over the goal post at C. At what distance s from the goal post will the football strike the ground at B? 34 A golf ball is struck with a velocity of 80 ft/s as shown. Determine the distance d to where it will land.
35 Determine the horizontal velocity V A of a tennis ball at A so that it just clears the net at B. Also, find the distance s where the ball strikes the ground.