Question: A body is projected into air with a velocity (3i^+4j^+5k^)m/s. Taking the X−Y plane as a base and the Z axis as vertical, the range of projectile (g=10m/s2).
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- A. 10 m
- B. 5 m
- C. 15 m
- D. 20 m
Solution:
Initial velocity components
\[
\vec{v} = 3\hat{i} + 4\hat{j} + 5\hat{k} \text{ m/s}
\]
Acceleration due to gravity
\[
g = 10 \text{ m/s}^{2}
\]
Time of flight
\[
T = \frac{2 \times 5}{10} = 1 \text{ s}
\]
Horizontal velocity
\[
\vec{v}_{\text{horizontal}} = \sqrt{3^2 + 4^2} = 5 \text{ m/s}
\]
Range of the projectile in the X-Y plane
\[
R = \vec{v}_{\text{horizontal}} \times T = 5 \text{ m/s} \times 1 \text{ s} = 5 \text{ m}
\]