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# Determine the Speed at Which the Basket Ball at a Must Be Thrown at an Angle 30o So that If Makes It to the Basket at B. Also Find at What Speed It Passes Through the Hoop. - Engineering Mechanics

Answer in Brief

Determine the speed at which the basket ball at A must be thrown at an angle 30o so that if makes it to the basket at B.
Also find at what speed it passes through the hoop. Advertisement Remove all ads

#### Solution

Given : θ=30o
To find : Speed at which basket ball must be thrown
Solution :
Assume that the basket ball be thrown with initial velocity u and it takes time t to reach B
HORIZONTAL MOTION
Here the velocity is constant
8 = ucos30 x t
t=8/(ucos30)=9.2376/u……..(1)
vB = ucos30 (Since velocity is constant in horizontal motion) ………(2)
VERTICAL MOTION
Initial vertical velocity (uv) = usin30 =0.5u …….(3)
Vertical displacement(s) = 2.4 - 1.2 = 1.2
t=9.2376/u
Using kinematical equation :
s = ut + 1/2 x at2
1.2=u/2x9.2376/u-1/2x9.81x((9.2376)/u)^2
u2=122.4289
u=11.0648 m/s
uv=0.5u (From 3)
uv = 0.5 x 11.0648
= 5.5324 m/s
Using kinematical equation
vv2 = uv2 + 2as
vv2 = 5.53242 - 2 x 9.81 x 1.2
vv = 2.6622 m/s
vh = 11.0648cos30 = 9.5824 m/s (From 2)
v_B=sqrtV_v^2+v_h^2
vB = 9.9441 m/s

apha=tan^-1((2.6577)/(9.5824))
= 15.5015°
Speed at which the basket-ball at A must be thrown = 11.0648 m/s (30° in first quadrant)
Speed at which the basket-ball passes through the hoop = 9.9441 m/s(15.5015° in fourth quadrant)

Concept: Motion Curves (a-t, v-t, s-t curves)
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