A projectile is shot from the ground at a velocity of $86 \frac{m}{s}$ $86 m/s$ at an angle of $\frac{π}{3}$ $pi/3$ . How long will it take for the projectile to land?

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A projectile is shot from the ground at a velocity of $86 \frac{m}{s}$ $86 m/s$ at an angle of $\frac{π}{3}$ $pi/3$ . How long will it take for the projectile to land?

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Answer 1 · 2016-10-21T19:56:30

Time = 14.5 s

Explanation:

We use the vertical direction to determine the time in the air.

$y = y_{0} + v_{0 y} t + \frac{1}{2} a_{y} t^{2}$ $y = y_0 + v_(0y)t + 1/2a_yt^2$

In this case
$y = 0$ $y=0$
$y_{0} = 0$ $y_0=0$
$v_{0 y} = 82 sin (\frac{π}{3})$ $v_(0y)=82sin(pi/3)$
$a_{y} = - g$ $a_y=-g$
So we have
$0 = 0 + 82 t sin (\frac{π}{3}) - \frac{1}{2} g t^{2}$ $0=0+82tsin(pi/3)-1/2 g t^2$
So $t = 0$ $t=0$
or $t = \frac{2 \cdot 82 \cdot sin (\frac{π}{3})}{g} = \frac{2 \cdot 82 \cdot \sqrt{3}}{2 \cdot 9.8} = 14.5 s$ $t=(2*82*sin(pi/3))/g=(2*82*sqrt3)/(2*9.8)=14.5 s$

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A projectile is shot from the ground at a velocity of $86 \frac{m}{s}$ $86 m/s$ at an angle of $\frac{π}{3}$ $pi/3$ . How long will it take for the projectile to land?

1 Answer

Explanation:

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A projectile is shot from the ground at a velocity of $86 \frac{m}{s}$ $86 m/s$ at an angle of $\frac{π}{3}$ $pi/3$ . How long will it take for the projectile to land?