Answer to Question #177457 in Physics for Maria

Question

A ball that was projected up at an angle of θ degrees with the horizontal has a flight time of 5.0s and covers a range of 49.0 m. Find (a) the time it took to reach the maximum height, (b) to the horizontal and vertical components of it's initial velocity, (c) it's initial velocity, (d) the angle θ at which it was projected, and (e) the maximum height it reached.

Answer 1

(a) Find the time it took to reach the maximum height. Assuming no air friction, it took half of the time o reach the maximum height and 50% of time to fall, so, the answer is 2.5 s.

(b) The horizontal component of its initial velocity can be found from the time and range:

$$v_h=\frac Rt=9.8\text{ m/s}.$$

The vertical can be found from the time of flight only:

$$v_v=gt=9.8·2.5=24.5\text{ m/s}.$$

(c) Its initial velocity can be calculated by Pythagorean theorem:

$$v=\sqrt{v_v^2+v_h^2}=26.4\text{ m/s}.$$

(d) The angle θ at which it was projected, and (e) the maximum height it reached:

$$\theta=\arctan\frac{v_v}{v_h}=68.2º.$$