Projectile Motion Numerical

                   Projectile Motion Numerical

SINGLE CORRECT CHOICE TYPE.

1. A cannon ball has the same range R on a horizontal plane for two angles of projection. If h1 and h2 are the greatest heights in the two paths for which this is possible, then
a) R=h1h2                  b) R=4(h1h2)1/2         c) R=(h1h2)1/3       d) R=(h1h2)1/4

2. A cricket ball is hit at 30ᵒ with the horizontal with kinetic energy K. The kinetic energy at the highest point is
a) 0                                   b) K/4                             c) K/2                      d) 3K/4

3. A particle is projected at an angle of elevation α and after t sec it appears to have an angle of elevation β as seen from the point of projection. The initial velocity will be
a) gt/2sin(α-β)             b) gtcosβ/2sin(α-β)        c) sin(α-β)/gt        d) 2sin(α-β)/gtcosβ

4. Two balls are thrown at the same time with the same speed (10 m/s). One ball is thrown straight up and the other ball is thrown at an angle of 45°. Which ball hits the ground first?
A) The ball thrown straight up                    B) The ball thrown at an angle
C) Both hit at the same time                        D)Not enough information to tell

5. A ball is kicked 10 m/s horizontally off a cliff. After 1 second, its speed is approximately
 a. 10 m/s                   b. 14 m/s                        c. 20 m/s                             d. 28 m/s

6. In the absence of air resistance, a ball of mass m is thrown straight up and reaches a height of 10 m. The net force on the ball half-way up (at 5 m up) is
 a. mg/4                     b. mg/2                            c. mg                                     d. 2mg

7. The greatest range of a particle, projected with a given velocity on an inclined plane, is x times the greatest vertical altitude above the inclined plane. Find the value of x ;
A. 2
B. 4
C. 3
D. 1/2

8. A person throws vertically n balls per second with the same velocity. He throws a ball whenever the previous oneis at its highest point. The height to which the ball rise is :
a) g/n^2
b) 2gn
c) g/2n^2
d) 2gn^2

9. A particle moves in x - y plane according to the equations x = 3cos4t and y = 3(1 - sin4t). The distance travelled bythe particle in 2 sec is (where x and y is in meter)
a) 48m
b) 24m
c) 48√2 m
d) 24√2 m.

10. A particle is projected at an angle of elevation α and after t seconds it appears to have an angle of elevation β asseen from point of projection. The initial velocity will be
A) gt / 2sin(α -β)
B) gt cosβ / 2sin(α - β)
C) Sin(α -β) / 2gt
D) 2sin(α - β) / gtcosβ.

11. A particle is projected at angle 37º with the inclined plane in upward direction with speed 10 m/s. Theangle of inclination is given 53º. Then the maximum height attained by the particle from the incline plane
will be
A) 3m
B) 4m
C) 5m
D) zero

12. For a stone thrown from the tower of unknown height, the maximum range for a projection speed of 10m/s is obtained for a projection angle of 30º. The corresponding distance between the foot of the tower
and the point of landing of the stone is
A) 10m
B) 20m
C) (20/√3)m
D) (10/√3)m.

13. A cricket ball is hit at 30º with the horizontal with kinetic energy K. The kinetic energy at the highest
point is
A) 0
B) K/4
C) K/2
D) 3K/4.

14. A body of mass m is projected at an angle of 45º with the horizontal with velocity u. If air resistance is
negligible, then total change in momentum when it strikes the ground is
A) 2mu
B) √2 mu
C) mu
D) mu / √2.

15. A particle is projected with speed 10 m/s at an angle 60º with the horizontal. Then the time after which
its speed becomes half of its initial is:
A) 1/2 sec
B) √3 /2 sec
C) 1 sec
D)2/3sec

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