1. (a) If you throw a golf ball straight up at a velocity vy, how long dos take
ID: 2287919 • Letter: 1
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1. (a) If you throw a golf ball straight up at a velocity vy, how long dos take to come back down? (b) [If a golf ball moves horizontally with a velocity vr, how far does it go in time t? (c) If you throw a golf ball with an initial vertical velocity vy and an initial horizontal velocity vr, how far away does it strike the ground, assuming level ground? 2. Estimate the initial vertical velocity of the piano in the video at https://www.youtube.com/ watch?v=hZrCEkCk6HL Explain how you got your answer 3. The steam-powered catapult on the USS Abraham Lincoln can accelerate an F-18 Hornet to a speed of 170 knots. The deck height of this carrier is h 26 m. If the pilot forgets to start the engines (unlikely) and falls asleep during the launch (even more unlikely) the Hornet becomes nothing more than a streamlined projectile. How far does this projectile go before hitting the water? 4. You ride a unicycle in a straight line at constant speed v. The radius of the wheel is r (a) What is the instantaneous acceleration (magnitude and direction) of a point at the top of the wheel? (b) What is the instantaneous acceleration (magnitude and direction) of a point at the bottom of the wheel? 5. A good sports car can manage a lateral acceleration of 1.1g's. How fast can this car go around a flat freeway onramp with a radius of 38 meters? 6. If the radius of a highway corner is increased by a factor of two, by how much is the maximum safe speed increased? 7. The range equation, 2 sin(20) is valid for negligible air resistance and flat horizontal ground. The factor of 2 means that there are generally two possible angles which can reach any valid range. For example, projectiles launched with equal velocities at 60° and at ,-30° will land at the same spot. The two projectiles will not take the same time, though. During the 1980's, the US Army was actually working on an artillery system that utilized this idea. The howitzer would fire two shells: the first at the higher angle, then some precise time interval t later the second at the lower angle. If they got t right, both shells would hit the target at the same time Derive an equation for . Your answer should depend on R, u, , and . (Somewhat interestingly, it does not depend on g...) The project was abandoned soon after the Soviet Union collapsed, since after the collapse nobody could figure out who they'd need to shoot at with such heavy artilleryExplanation / Answer
Initial velocity = Vy
final velocity at the highest point = 0
v = u - gt
= = Vy - gt
t = Vy / g
the same time is taken for the downward journey also
so total time = 2Vy/g
Horizontal velocity = Vx
distance travelled in time t = vt = Vx t
the 3rd case is a projectile ,
horizontal distance = horizontal velocity x time of flight
time of flight as calculated in the above case = 2Vy/g
so range = (2Vy/g )x Vx
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