Question

An object is being shot from a horizontal ground at an incline angle of 30 degree with respect to the ground at a speed of 49 m/s. Find the duration in seconds that the object is above the height of 13 m. Give your answer with one decimal place.

Answer 1

The equation of motion of an object is given by

$$y=v_0\sin\theta t-gt^2/2\\ y=49\sin30^\circ t-9.8t^2/2\\ y=24.5t-4.9t^2$$

At the height 13 m we have

$$13=24.5t-4.9t^2$$

Roots of this equation

$$t_1={0.60\:\rm s,}\;t_2=4.40\:\rm s$$

Hence, duration in seconds that the object is above the height of 13 m

$$\Delta t=t_2-t_1\\ =4.40-0.60=3.8\:\rm s$$