J J Science Academy - Test Paper

1. A particle is projected with an initial velocity of $20 \, \text{m/s}$ at an angle of $30^\circ$ with the horizontal. What is the maximum height reached by the particle? (Take $g=10 \, \text{m/s}^2$)

(1) $2.5 \, \text{m}$

(2) $5 \, \text{m}$

(3) $10 \, \text{m}$

(4) $15 \, \text{m}$

2. The range of a projectile fired at an angle $\theta$ with the horizontal is $R$. If the initial velocity is $u$, then the range is given by:

(1) $R = \frac{u^2 \sin(2\theta)}{g}$

(2) $R = \frac{u \sin(2\theta)}{g}$

(3) $R = \frac{u^2 \cos(2\theta)}{g}$

(4) $R = \frac{u \cos(2\theta)}{g}$

3. A ball is thrown horizontally from the top of a tower $45 \, \text{m}$ high with a speed of $10 \, \text{m/s}$. How far from the base of the tower will it strike the ground? (Take $g=10 \, \text{m/s}^2$)

(1) $10 \, \text{m}$

(2) $20 \, \text{m}$

(3) $30 \, \text{m}$

(4) $40 \, \text{m}$

4. For a projectile, the maximum height $H$ and range $R$ are related by:

(1) $R = 4H \cot\theta$

(2) $H = 4R \cot\theta$

(3) $R = H \cot\theta$

(4) $H = R \cot\theta$