Determine the distance from point C to the point on the horizontal surface D, if a ball is fired from a point A at the bottom of the inclined plane as shown in the figure. The mass of the ball is 4 kg ball and is of negligible size. The initial velocity of the ball is 20 m/s up the smooth inclined plane. Also, what is the velocity when it strikes the surface.

1) 36.9 m & 20 m/s
2) 32.5 m & 34 m/s
3) 42.5 m & 26 m/s
4) 61.5 m & 50 m/s

Assuming the datum at A and applying the principle of conservation of energy we have :
T_A + V_A = T_B + V_B
1/2(4)(20)² + 0 = 1/2(4)(v_B)² - 4(9.81)3
v_B = 18.47 m/s
So, the velocity of the ball at Bis v_B = 18.47 m/s

The time taken for the ball to travel from B to D can be found out by the following equation:
s = s_o + v_o t + 1/2 a_c t²
- 3 = 0 + 18.47 (3/5) t + 1/2 (-9.81) t²
t = 2.5 s

So the time taken for the ball to reach the point D is
t = 2.5 s

The distance travelled by the ball horizontally to reach point D is given by the equation:
s = s_o + v_o t
d = 0 + 18.47 ( 4/5) t = 36.9 m

So the distance travelled by the ball horizantally to reach point D is d = 36.9 m

Datum A :
T_A + V_A = TD + VD
1/2 (4) (20)² + 0 = 1/2 (4) (v_D)² + 0
v_D = 20 m/s

So the velocity with which the ball strikes the surface at D is v_D = 20 m/s and also the distance travelled by it from C to reach point D, d = 36.9 m