ap physics work and energy

Question

A 50.0 kg cannonball is launched off a cliff at a speed of 25.0 m/s. How much kinetic energy does the cannonball have when it has fallen 57.0 m off the cliff?

Answer 1

Assumptions: g = -9.8m/s², air resistance is negligible, initial velocity in Y direction is 0 m/s

Givens: mass (m) = 50.0 kg; initial x velocity (v_x) = 25 m/s; initial y velocity (v_y) = 0 m/s

Equations:

v_y² = v_o² + 2*g*(y-y₀) (this determines the velocity in the Y direction after 57 m of freefall)

v² = v_x² + v_y² (this uses Pythagorean theorem to find the total velocity)

Kinetic Energy (K.E,) = 1/2 * m * v²

Solve for v_y: v_y = √(0 m/s ² + (2 * (-9.8 m/s² ) * ( -57 m - 0 m)))

v_y = 23.63 m/s

Solve for total velocity using x and y velocities:

v = √(25 m/s ² + 23.63 m/s ²) = 34.4 m/s

solve for K.E.

K.E. = (1/2) * (50 kg) * ((34.4 m/s) ²) = 29,584 Joules

check units on the KE equation: kg * (m/s) * (m/s) = kg*m² / s² = Joules