Question

A pumpkin with a mass of 3.3 kg is launched from a catapult at an initial height of 3.8 m off the ground, with an initial speed of 13.9 m/s. What height is the pumpkin at when the speed is half its initial speed? Round your answer to 2 decimal places.

Answer 1

Answer:

11.2m

Explanation:

Suppose the pumpkin is launched vertically and the speed of 13.9 m/s is absolutely vertical. As the pumpkin rises up, its kinetic energy is converted to potential energy, let the reference point be the round, we can create the following equation from the law of energy conservation:

$E_1 + P_1 = E_2 + P_2$

$0.5mv_1^2 + mgh_1 = 0.5mv_2^2 + mgh_2$

we can substitute $g = 9.8m/s^2, v_1 = 13.9m/s, v_2 = 0.5v_1 = 0.5*13.9 = 6.95 m/s, h_1 = 3.8$

We can also divide both sides by m and 0.5

$13.9^2 + 2*9.8*3.8 = 6.95^2 + 2*9.8*h_2$

$19.6h_2 = 219.3875$

$h_2 = 11.2m$