Answer to Question #255501 in Physics for Monieth Dela Cruz

Question

Firemen are shooting a stream of water at a burning building. A high pressure hose shoots out the water with the speed of 25.0 m/s as it leaves the hose nozzle. Once it leaves the hose, the water moves in projectile motion. The firemen adjust the angle of elevation of the hose until the water takes 3.00 s to reach a building 45.0 m away. You can ignore air resistance; assume that the end of the hose is at the ground level. (a) Find the angle of elevation of the hose. (b) Find the speed and acceleration of the water at the highest point in its trajectory. (c) How high above the ground does the water strike the building, and how fast is it moving just before it hits the building?

Answer 1

a) Find the range and use it to express the angle:

$$R=v\cos\theta·t,\\\space\\ \theta=\arccos\frac{R}{vt}=53°.$$

b) The speed at the highest point is 25 m/s, the acceleration is 9.8 m/s².

c) The height is

$$H=\frac{v^2\sin^2\theta}{2g}=20.3\text{ m},\\\space\\ v=\sqrt{v_x^2+v_y^2}=\sqrt{(v\sin\theta)^2+(v\cos\theta)^2},\\ v=25\text{ m/s}.$$