Q. 51

Expert-verifiedFound in: Page 108

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

A tennis player hits a ball 2.0 m above the ground. The ball

leaves his racquet with a speed of 20.0 m/s at an angle 5.0° above the horizontal. The horizontal distance to the net is 7.0 m, and the net is 1.0 m high. Does the ball clear the net? If so, by how much? If not, by how much does it miss?

Yes, the ball clear the net by .

The initial vertical position of the ball is , the initial speed of the ball is , the angle of projection is , the horizontal distance travelled by the ball is and the height of the net is .

The formula to calculate the horizontal distance travelled by the ball is given by

Here, is the horizontal distance travelled, is the initial speed of the ball, is the projection angle and is the time required.

Substitute for , for and for into equation (1) and solve to calculate the time required.

The formula to calculate the final vertical height of the ball is given by

Here, are the final vertical height, initial vertical height and acceleration due to gravity respectively.

Substitute for , for , for , for and for into equation (2) to calculate the final vertical height of the ball.

The formula to calculate the distance between the net and the final vertical position of the ball is given by

Here, is the height of the net.

Substitute for and for into equation (3) to calculate the required difference in height.

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