BackA hot-air balloonist, rising vertically with a constant velocity of magnitude m/s, releases a sandbag at an instant when the balloon is m above the ground (Fig. E). After the sandbag is released, it is in free fall. What is the greatest height above the ground that the sandbag reaches?
(I) If a car rolls gently (v₀ = 0) off a vertical cliff, how long does it take it to reach 55 km/h?
A rock is thrown vertically upward with a speed of 27.0 m/s from the roof of a 31.0-m-tall building. The rock doesn't hit the building on its way back down and lands in the street below. (a) What is the speed of the rock just before it hits the street? (b) How much time elapses from when the rock is thrown until it hits the street?
A person holds a bill of length vertically above her hand and releases it from rest. Assuming negligible air resistance and that the acceleration due to gravity is , approximately how much time does it take for the bill to fall completely beyond her grasp?
A typical laboratory centrifuge rotates at 4000 rpm. Test tubes have to be placed into a centrifuge very carefully because of the very large accelerations. For comparison, what is the magnitude of the acceleration a test tube would experience if dropped from a height of 1.0 m and stopped in a 1.0-ms-long encounter with a hard floor?
If a flea can jump straight up to a height of m, what is its initial speed as it leaves the ground?
A ball is thrown straight up from the ground. At the very top of its trajectory, what is the direction of its vector?
Two children are playing on two trampolines. The first child bounces up one-and-a-half times higher than the second child. The initial speed upwards of the second child is 4.0 m/s. What is the initial speed of the first child?
(III) A toy rocket moving vertically upward passes by a 2.0-m-high window whose base is 8.0 m above the ground. The rocket takes 0.15 s to travel the 2.0 m height of the window. What was the launch speed of the rocket, and how high will it go? Assume the propellant is burned very quickly at blastoff.
A tennis ball on Mars, where the acceleration due to gravity is and air resistance is negligible, is hit directly upward and returns to the same level s later. How high above its original point did the ball go?
A 200 kg weather rocket is loaded with 100 kg of fuel and fired straight up. It accelerates upward at 30 m/s² for 30 s, then runs out of fuel. Ignore any air resistance effects. What is the rocket's maximum altitude?
A person holds a bill of length vertically at the top edge. If the bill is released and allowed to fall freely under gravity, approximately how much time does it take for the bottom edge of the bill to fall beyond her grasp (i.e., to fall )? Assume acceleration due to gravity is and neglect air resistance.
An object is dropped from rest and falls freely under gravity for seconds. How far does it fall? (Assume and neglect air resistance.)
(II) Pelicans tuck their wings and free-fall straight down when diving for fish. Suppose a pelican starts its dive from a height of 16.0 m and cannot change its path once committed. If it takes a fish 0.20 s to perform evasive action, at what minimum height must it spot the pelican to escape? Assume the fish is at the surface of the water.
A -kg rocket blasts off vertically from the launch pad with a constant upward acceleration of m/s2 and feels no appreciable air resistance. When it has reached a height of m, its engines suddenly fail; the only force acting on it is now gravity. What is the maximum height this rocket will reach above the launch pad?