Answer to Question #166001 in Astronomy | Astrophysics for wadzani

Question

a stone propelled from a catapault with a speed of 50m/s attains a height
of 100 m. calculate;the time of flight,the angle of projection,the range attained

Answer 1

a) Time of flight for a projectile, $T=2Usin\frac{\theta}{g}$

$U = 50 m/s$

$\theta = ?$

$g = 10 m/s^2$

However, maximum height, $H = U^2sin^2$$\frac{\theta}{2g}$

$H = 100 m$

Hence, $100 = 50^2 sin^2\frac{\theta}{2\times10} ​$

$sin^2\theta = \frac{2\times10\times100}{50^2}= 0.8$

$sin\theta = 0.8944$

Therefore, $T = \frac{2\times50\times0.8944}{10} = 8.9 s$

b) $sin\theta = 0.8944$

Using Natural Sine Table (Trigonometrical Tables)

$\theta$, angle of projection = 63,4^o1'

c) Range, $R = \frac{U^2sin2θ}{g} = \frac{50^2sin(2\times63.4^o1')}{10} = 250 \times 0.8007 = 200.2 m$

Answer: a) T = 8.9 s; b) $\theta$ = 63,4^o1'; c) R = 200.2 m.