A baseball thrown at an angle of 55.0 ∘ above the horizontal strikes a building 17.0 m away at a point 5.00 m above the point from which it is thrown. Ignore air resistance. (A)Find the magnitude of the initial velocity of the baseball (the velocity with which the baseball is thrown). (B)Find the magnitude of the velocity of the baseball just before it strikes the building. (C)Find the direction of the velocity of the baseball just before it strikes the building.

(A) Initial velocity of baseball is 14.97 m/s.

(B) Velocity of baseball just before hitting the wall is 11.16 m/s.

(C) The baseball is moving in downward direction just before striking the wall.  

Explanation:

Let u m/s be the initial velocity of the baseball. According to the problem, the ball makes an angle of 55⁰ with respect to horizontal direction, Hence, the components of initial velocity along horizontal (u₁) and vertical direction (u₂) are:

u₁ = u cos 55⁰

u₂ = u sin 55⁰

The equation of motion is:

d = ut + 0.5at²

(A) Since baseball has no acceleration along horizontal direction, the horizontal distance covered by the baseball is:

d = u₁t

17 = u cos 55⁰ x t

29.64 = ut                  ......(1)

In vertical direction, acceleration due to gravity(g) is acted on the baseball, so the equation becomes:

h = u₂t - 0.5gt²

5 = u sin 55⁰ t - 0.5 x 9.8 x t²       .......(2)

Substitute equation (1) in equation (2);

5 = 29.64 x 0.82 - 4.9 x t²

t = 1.98 s

Substitute the value of t in equation (1):

29.64 = u x 1.98

u = 14.97 m/s

(B) Let v be the final velocity of the baseball. The horizontal component of final velocity of baseball remains same as the initial velocity. Thus,

v₁ = u cos 55⁰ = 14.97 x cos 55⁰ = 8.58 m/s

The vertical component of final velocity of the baseball is:

v₂ = u sin 55⁰ - gt = 14.97 x sin 55⁰ - 9.8 x 1.98 = -7.14 m/s

The resultant final velocity of the baseball is:

v =

v =

v = 11.16 m/s

(C) The direction of the baseball just before hitting the wall is:

θ = tan⁻¹(v₂/v₁)

θ = tan⁻¹(-7.14/ 8.58)

θ = -39.76⁰

Thus, the baseball is moving in the downward direction.

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