A projectile is shot from the ground at a velocity of $5 \frac{m}{s}$ $5 m/s$ at an angle of $\frac{5 π}{12}$ $(5pi)/12$ . How long will it take for the projectile to land?

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Answer 1 · 2017-01-30T08:18:57

The answer is $0.99 s$ $0.99 s$

Resolving in the vertical direction ${↑ ⏐ ⏐}^{+}$ $uarr^+$

$u = 5 sin (\frac{5}{12} π) m s^{- 1}$ $u=5sin(5/12pi) ms^-1$

$a = - g m s^{- 2}$ $a=-g ms^-2$

$s = 0 m$ $s=0m$

We use the equation

$s = u t + \frac{1}{2} a t^{2}$ $s=ut+1/2at^2$

$0 = 5 sin (\frac{5}{12} π) \cdot t - \frac{g}{2} t^{2}$ $0=5sin(5/12pi)*t-g/2t^2$

$t (5 sin (\frac{5}{12} π) - \frac{g}{2} t) = 0$ $t(5sin(5/12pi)-g/2t)=0$

Therefore,

$t = 0$ $t=0$ , this is when the projectile is shot

and

$5 sin (\frac{5}{12} π) - \frac{g}{2} t = 0$ $5sin(5/12pi)-g/2t=0$

$t = \frac{10}{g} sin (\frac{5}{12} π)$ $t=10/gsin(5/12pi)$

$t = \frac{10}{9.8} sin (\frac{5}{12} π) = 0.99 s$ $t=10/9.8sin(5/12pi)=0.99s$

A projectile is shot from the ground at a velocity of 5 m/s5ms5 m/s at an angle of (5pi)/125π12(5pi)/12. How long will it take for the projectile to land?