First slide

Projection Under uniform Acceleration

Question

The driver of a car moving towards a rocket launching with a speed of 6 ms^-1 observed that the rocket is moving with speed of 10 ms^-1.The upward speed of the rocket as seen by the stationary observer is nearly

Moderate

A

4 ms^-1
B

6 ms^-1
C

8 ms^-1
D

11 ms^-1

Solution

Suppose the car is moving horizontally along positive x-axis with velocity $\large \vec v_c=6\hat im/s$ . Vertical velocity of the rocket is positive y-axis relative to a stationary observer. $\large \vec v_R=v_R\hat jm/s$ .
velocity of the rocket relative to the car = $\large \overrightarrow {{v_{R/c}}}=\vec v_R-\vec v_c=(v_R\hat j-6\hat i)m/s$
$\large \therefore$ $\large \left| {\overrightarrow {{v_{R/c}}} } \right| = \sqrt {v_R^2 + {6^2}}$
$\large \therefore$ $\large {(10)^2} = v_R^2 + 36 \Rightarrow {v_R} = 8m/s$

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