In this question, use \(g=10\,\)m\,s\(^{-2}\).
In cricket, a fast bowler
projects a ball at \(40\,\)m\,s\(^{-1}\) from a point \(h\,\)m above the ground,
which is horizontal, and at an angle \(\alpha\) above the
horizontal.
The trajectory is such that the ball will
strike the stumps at ground level a horizontal distance
of \(20\,\)m from the
point of projection.
- Determine, in terms of \(h\), the two possible values of \(\tan\alpha\).
Explain which of these two values is the more appropriate one, and
deduce
that the ball hits the stumps after approximately half a second.
- State the range of values of \(h\) for which the bowler
projects the ball below the horizontal.
- In the case \(h=2.5\), give an approximate value in degrees,
correct to two significant figures, for
\(\alpha\). You need not justify the accuracy of your
approximation.
[You may use the small-angle approximations \(\cos\theta \approx 1\) and
\(\sin\theta\approx \theta\).]