Kinematics 2-D A rural mail carrier leaves the post office and drives 22.0 km in a northerly direction to the next town. She then drives in a direction sixty degrees south of east for 47.0 km to another town. What is her displacement. Answer: 30.0 km -38.5 degrees below the x axis RoessBoss 1 2012-08-15 16:12:54 1/11 Kinematics2Dproblems.pdf (#2)
Kinematics 2D An airplane trip involves three legs, with two stopovers. The first leg is due east for 620 km, the second leg is southeast (45 degrees) for 440km, and the third leg is at 53 degrees south of west, for 550 km. What is the plane s total displacement Answer: 960 km at -51 degrees below the x axis RoessBoss 2 2012-08-15 16:12:54 2/11 Kinematics2Dproblems.pdf (2/11)
Projectile motion A movie stunt driver on a motorcycle speeds horizontally off a 50.0 m high cliff. How fast must the motorcycle leave the cliff-top if it is to land on level ground below, 90.0 m from the base of the cliff. Answer: 3.19 s, 28.2 m/s RoessBoss 3 2012-08-15 16:12:55 3/11 Kinematics2Dproblems.pdf (3/11)
Projectile motion A football is kicked at an angle of 37 with a velocity of 20.0 m/s. Calculate a) the maximum height, b) the time of travel before the football hits the ground, c) how far away it hits the ground, d) the velocity vector at the maximum height, and e) the acceleration vector at maximum height. Assume the ball leaves the foot at ground level, and ignore air resistance. Answer: 1.22 s, 7.35 m, 2.45 s, 39.2 m, 16.0m/s, 9.80 m/s^2 RoessBoss 4 2012-08-15 16:12:55 4/11 Kinematics2Dproblems.pdf (4/11)
Projectile motion A) Derive a formula for the horizontal range R of a projectile in terms of initial velocity V0 and angle ø, The horizontal range is defined as the horizontal distance the projectile travels before returning to its orignal height, which is typically the ground; that is y(final)= Yo. Suppose one of Napoleon s cannons had a muzzle velocity Vo, of 60.0 m/s. At what angle should it have been aimed (ignore air resistance) to strike a target 320 m away? Answer: 30.3 or 59.7 degrees RoessBoss 5 2012-08-15 16:12:55 5/11 Kinematics2Dproblems.pdf (5/11)
Projectile motion Suppose the football [in the kicked football example (37 )] was a punt and left the punters foot at height of 1.00 m above the ground. How far did the football travel before hitting the ground. Set Xo= 0 and Yo= 0 Answer: 2.35s, 40.5 m RoessBoss 6 2012-08-15 16:12:55 6/11 Kinematics2Dproblems.pdf (6/11)
Kinematics 1D A rescue plane wants to drop supplies to isolated mountain climbers on a rocky ridge 200 m below. If the plane is traveling horizontally with a speed of 250 km/h, A) how far in advance of the recipients (horizontal distance) must the goods be dropped B) Suppose instead that the plane releases the supplies a horizontal distance of 400 m in advance of the mountain climbers. What vertical velocity should they give the supplies (up or down) so that they arrive precisely at the climbers position C) with what speed do the supplies land in the latter case? Answer: 6.39 s, -6.1 m/s, -63 m/s RoessBoss 7 2012-08-15 16:12:56 7/11 Kinematics2Dproblems.pdf (7/11)
Uniform Circular motion A 150 g ball at the end of a string is revolving uniformly in a horizontal circle of radius 0.600 m. The ball makes 2.00 revolutions in a second. What is its centripetal acceleration? Answer: 7.54 m/s, 94.8 m/s^2 RoessBoss 8 2012-08-15 16:12:56 8/11 Kinematics2Dproblems.pdf (8/11)
Uniform Circular motion The Moon s nearly circular orbit about the Earth has a radius of about 384,000 km and a period T of 27.3 days. Determine the acceleration of the Moon towards the Earth. Answer: 2.72 E -3 m/s^2, 2.78 E -4g RoessBoss 9 2012-08-15 16:12:56 9/11 Kinematics2Dproblems.pdf (9/11)
Relative Velocity A boat s speed in still water is 1.85 m/s. If the boat is to travel northward directly across a river whose current has a velocity is 1.20 m/s toward the west, at what angle must the boat head? Answer: 40.4 RoessBoss 10 2012-08-15 16:12:56 10/11 Kinematics2Dproblems.pdf (10/11)
Relative Velocity The same boat now head directly across the stream whose current is still the same as previous. A) what is the velocity (magnitude and direction) of the boat relative to the shore? B) If the river is 110 m wide, how long will it take to cross and how far downstream will the boat be then? Answer: 2.21 m/s, 0.6486, 72 m RoessBoss 11 2012-08-15 16:12:56 11/11 Kinematics2Dproblems.pdf (11/11)