First slide

Relative velocity in 1-d

Question

Imagine yourself standing in an elevator which is moving with an upward acceleration $a = 2 m / s^{2}$ .A coin is dropped from rest from the roof of the elevator, relative to you.
The roof to floor height of the elevator is 1.5 m. (Take $g = 10 m / s^{2}$ ). rind the velocity of the coin relative to you when it strikes the base of the elevator.

Moderate

A

3 m/s
B

6 m/s
C

2 m/s
D

1.5 m/s

Solution

$Using v_{r}^{2} = u_{r}^{2} + 2 a_{r} s, u_{r} = 0$
$\begin{array}{l} a_{r} = g - (- a) = (g + a) \\ v_{r}^{2} = 0 + 2 (g + a) \cdot h \\ v = \sqrt{2 (g + a) h} = \sqrt{2 \times 12 \times 1.5} = 6 m / s \end{array}$

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