Question

A T-shirt cannon launches a shirt at 5.00 m/s from a platform height of 3.00 m from ground level. How fast will the shirt be traveling if it is caught by someone whose hands are

(a) 1.00 m from ground level?
(b) 4.00 m from ground level? Neglect air drag.

Answer 1

Using conservation of energy principles, the final speeds for a T-shirt shot from a cannon caught at 1.00 m and 4.00 m from ground level are calculated to be 7.67 m/s and 5.10 m/s respectively, neglecting air drag.

Step-by-step explanation:

The question relates to the physics concepts of projectile motion and conservation of energy. Neglecting air resistance, we can determine the final velocity of the T-shirt when caught at different heights using the conservation of energy principle. Once launched, the T-shirt has an initial kinetic energy and potential energy relative to the ground level. As it falls, the potential energy decreases and is converted into kinetic energy, thus increasing the shirt's speed until it is caught.

To find the final speed when the T-shirt is caught 1.00 m from ground level, we use the following equation derived from the conservation of energy principle:

Initial Potential Energy + Initial Kinetic Energy = Final Potential Energy + Final Kinetic Energy

mgh + 0.5mv2 = mg(h - 1) + 0.5mvf2

Solving for vf, we find that the final velocity vf is 7.67 m/s.

Similarly, to find the final speed when the T-shirt is caught 4.00 m from ground level, the final velocity vf is calculated to be 5.10 m/s.