Question

At the base of a hill, a 90 kg cart drives at 13 m/s toward it then lifts off the accelerator pedal). If the cart just barely makes it to the top of this hill and stops, how high must the hill be?

Answer 1

Answer:

the height of the hill is 8.622 m.

Explanation:

Given;

mass of the cart, m = 90 kg

speed of the cart at the base, v = 13 m/s

Let the height of the hill = h

Apply the principle of conservation of energy, to determine the height of the hill.

¹/₂mv² = mgh

¹/₂v² = gh

$h= \frac{1}{2} \times \frac{v^2}{g} \\\\h = \frac{1}{2} \times \frac{13^2}{9.8} \\\\h = 8.622 \ m$

Therefore, the height of the hill is 8.622 m.