4. A cart is moving horizontally along a straight line with constant speed 30 m/s. A projectile is to be fired from the moving cart in such a way that it will return to the cart after the cart has moves 80 m. At what speed relative to the cart and at what angle to the horizontal must the projectile be fired?
(a) 13.1 m/s at θ = 90° (b) 13.1 m/s at θ = 45°
(c ) 15 m/s at θ = 60° (d) 20 m/s at θ = 30°
5. Two particles are projected from the same point on level ground simultaneously with the same velocity u but at the angles of projection (α-β) and (α+β) respectively (β < 45°). Which of the following statements will be true?
(a) They will have the same horizontal range if α = 45°
(b) They will reach their maximum heights at the time internal of 2υsinβ cosα/g
(c) They will be separated by the distance of 2u2/g (sin 2α cos 2β) when they reach the ground
(d) They are never in the same horizontal leval during their flights.
6. A particle is projected horizontally from the top of a tower. The radius of curvature ofits path at a point where its velocity is v is directly proportional to
a. v3
b. v2
c. v
d. 1/v