A student is standing on the open platform of a moving train at a speed of 10 m/s. The student throws a ball into the air along a path that, he judges to make an initial angle of 6 0 ∘ with the horizo

Question

A student is standing on the open platform of a moving train at a speed of 10 m/s. The student throws a ball into the air along a path that, he judges to make an initial angle of 6 0 ∘ with the horizontal and to be in line with the track. The professor, who is standing on the ground nearby, observes the ball to rise vertically. Find the height reached by the ball.

TestHub · Accepted Answer

For the professor to see the ball rise vertically, the ball's horizontal velocity relative to the ground must vanish:
$u cos 6 0^{\circ} = 10$ ,
so
$u = 20 m / s$
relative to the student. Vertical component:
$20 sin 6 0^{\circ} = 103$ $m / s;$ height
$= \frac{( 10 3 ) ^{2}}{2 \times 10} = \frac{300}{20} = 15 m$ .
Matches the printed answer (
$g = 10 m / s^{2}$
).

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