An object is projected upwards along a slope inclined at 45 degrees from the horizontal. The Initial speed is 8m/s and coefficient of friction is 0.3.

Question

The object comes to instantaneous rest before reaching the top of the inclined surface. Calculate

a) the distance the object moves before it comes to rest.

b) the time the object takes to come to rest.

c) the time taken for the object to return to its initial point.

Answer 1

a) You can use an energy balance: E_K,Before - W_F = E_P,After

E_K = 1/2 mv² E_p = mgh = mgdainθ W_F = F_fd = mgμcos(θ)d and solve for d

b) You know d, v_i, and v_f so d = (v_i + v_f)/2 * t solve for t

c) You can find v_f using E_P,Before - W_F = E_{K, after} and again use the same equation as in (b) to get t