How long does it take for the ball to reach the wall if it is 4.2 m away and what is the height at which the ball hits the wall?In a friendly game of handball, you hit the ball essentially at...

How long does it take for the ball to reach the wall if it is 4.2 m away and what is the height at which the ball hits the wall?

In a friendly game of handball, you hit the ball essentially at ground level and send it toward the wall with a speed of 14 m/s at an angle of 24 degrees above the horizontal.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The ball is struck at ground level and sent towards a wall with a speed of 14 m/s at an angle of elevation 24 degrees above the horizontal.

The initial velocity of the ball can be divided into two components, one parallel to the horizontal equal to 14*cos 24 and the other perpendicular to the horizontal equal to 14*sin 24 in the upward direction.

As the wall is 4.2 m away, the time taken by the ball to reach it is `4.2/(14*cos 24) ~~ 0.3284` seconds.

To determine the height at which the ball strikes the wall the acceleration due to gravity that is 9.8 m/s^2 in the vertically downwards direction has to be kept in mind. The height of the ball is equal to `14*sin 24*0.3284 - (1/2)*9.8*(0.3284)^2`

 `~~ 1.3415 m`

The balls takes approximately 0.3284 seconds to reach the wall and strikes it at a height 1.3415 m.

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

a) You need to remember the equation that puts in relation the distance, velocity and time such that:

`d = vt`

Since the problem provides the value of velocity and the total distance, hence, you need to substitute these values in equation above such that:

`t = d/v`

Considering the horizontal component of velocity yields:

`v_x = v cos 24^o`

`t = 4.2/(14*cos 24^o) => t = (4.2m)/(12.789 m/s) => t = 0.32 ``s`

Hence, evaluating the time taken for the ball to reach the wall yields `t = 0.32 s.`

b) You know that the ball hits the wall after `t = 0.32 ` s, hence, using the vertical component of velocity, you may evaluate the height reached by the ball when it hits the wall such that:

`h = v_y*t => h = 14*sin 24^o*0.32`

`h ~~ 1.82 m`

Hence, evaluating how high is the ball when it hits the wall yields `h ~~ 1.82 m.`

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