Question

A projectile is launched at ground level with an initial speed of 50.0m/s at an angle of 30° above the horizontal. It strikes a target above the ground 3.00 seconds later. What are the x and y distances from where the projectile was launched to where is lands?

Answer 1

Answer:

x = 129.9 m

y = 30.9 m

Explanation:

When an object is thrown into the air under the effect of the gravitational force, the movement of the projectile is observed. Then it can be considered as two separate motions, horizontal motion and vertical motion. Both motions are different, so that they can be handled independently.

Given data:

$v_{i}$ = 50 m/s

Angle = 30°

Time = t = 3 s

horizontal component of velocity = $v_{i_{x}}$ = $v_{i}$cos30°

$v_{i_{x}}$ = 50cos30°

$v_{i_{x}}$ = 43.3 m/s

Vertical component of velocity = $v_{i_{y}}$ = $v_{i}$Sin30°

$v_{i_{y}}$ = 50Sin30°

$v_{i_{y}}$ = 25 m/s

This is a projectile motion, and we know that in projectile motion the horizontal component of the velocity remain constant throughout his motion. So there is no acceleration along horizontal path.

But the vertical component of velocity varies with time and there is an acceleration along vertical direction which is equal to gravitational acceleration g.

Horizontal distance = x =  $v_{i_{x}}$t

x =  43.3*3

x = 129.9 m

Vertical Distance = y = $v_{i_{y}}$t -0.5gt²

y = 25*3 - 0.5*9.8*3²

y = 75 - 44.1

y = 30.9 m