Single Choice

A body is projected horizontally from a height with speed $$20\ m/sec$$. What will be its speed after $$5\ sec(g=10\ m/s^{2})$$:

A$$54\ m/s$$
Correct Answer
B$$20\ m/s$$
C$$50\ m/s$$
D$$70\ m/s$$

Solution

Along x-axis,
$$u_x=20m/s$$
$$g_x=0m/s^2$$
$$t=5sec$$
From 1st equation of motion,
$$v_x=u_x+g_xt$$
$$v_x=20+0\times 5$$
$$v_x=20m/s$$
Along y-axis,
$$u_y=0m/s$$
$$g_x=10m/s^2$$
$$t=5sec$$
From 1st equation of motion,
$$v_y=u_y+g_yt$$
$$v_y=0+10\times 5$$
$$v_y=50m/s$$
Velocity of of body after $$t=5sec$$,
$$\vec v=v_x\hat i+v_y\hat j$$
$$\vec v=20\hat i+50\hat j$$
The magnitude of the velocity is
$$v=|\vec v|=\sqrt{(20)^2+(50)^2}$$
$$v=\sqrt{2900}m/s$$
$$v=53.84\approx 54m/s$$
The correct option is A.

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