Serving at a speed of 170 km/h, a tennis player hits the ball at a height of 2.5 m and an angle θ below the horizontal. The service line is 11.9 m from the net, which is 0.91 m high.
Find the angle θ, in degrees, at which the ball just crosses the net.
At what distance, in meters, from the service line does the ball land?
a)
The tennis ball’s initial speed in the X and Y directions can be represented as,
Here, θ represents the angle at which the ball is hit.
The vertical distance covered by the ball can be represented as,
Here, y0, ay, and t represent the ball’s initial height, the ball’s vertical acceleration, and the time, respectively.
The ball’s vertical acceleration is the same as the acceleration because of the Earth’s gravity.
Thus,
Now, the horizontal distance covered by the ball can be represented as,
Here, the terms with the subscript x have their usual meaning but, in the X-direction.
The ball’s horizontal acceleration is zero. The ball’s initial horizontal distance is zero.
Substitute the relevant values.
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