Question

A ball is thrown from ground level so as to just clear a wall 4 metre high at a distance of 4m and falls at a distance of 14m from the wall. Find the magnitude and direction of Initial velocity of ball

Answer 1

Use the projectile trajectory equation to get tan(theta). By putting tan(theta) value in range formula , we get the value of initial velocity.
Detailed solution is in attachment.

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Answer 2

Given:

Height of the wall = 4m

Distance = 4m

Fall from distance = 14m

To Find:

Magnitude and direction of initial velocity of ball

Solution:

The ball passes through point 4,4

Range = 4 + 14 = 18m

Trajectory of the ball  = xtanФ ( 1- x/R)

where x = 4cm y = 4cm and R = 18cm

Thus,  

4 = 4tanФ ( 1- 4/18)

= 4 tanФ 7/9

or tanФ = 9.7 = o = tan 9/7 and R = 2u²sinФcosФ/g

18 = 2/9.8 × u² × 9/√130 × 7/√130

u = √182

Answer: The magnitude is √182