Question

Please I need help fast. Assignment is due soon.

1) A ball is thrown from the top of a building with an initial speed of 8.0 m/s at an angle of 35° above the horizontal. The building is 18 m tall.

a) How long is the ball in the air?

b) How far from the building does the ball land?

c) What is its impact speed?


2) A 65-kg person driving a car hits the gas, accelerating the car at a rate of 3.9 m/s^2. Find the magnitude and direction of the force exerted by the seat on the person's body. Remember to include both the horizontal and the vertical components.

Answer 1

(a) The time spent in the air by the ball is 1.5 seconds.

(b) The horizontal distance of the ball is 9.83 m.

(c) The impact speed of the ball is 20.37 m/s.

(2) The magnitude of the force is 253.5 N in horizontal direction.

Time of motion of the ball

The time of motion of the ball is calculated as follows;

h = vt + ¹/₂gt²

18 = 8sin(35)t + (0.5)(9.8)t²

18 = 4.589t + 4.9t²

4.9t² + 4.589t - 18 = 0

solve the quadratic equation using formula method,

t = 1.5 s

Horizontal distance of the projectile

X = vcosθ(t)

X = 8cos(35) x 1.5

X = 9.83 m

Impact speed of the projectile

vyf = vyi + gt

vyf = 8sin(35) + 9.8(1.5)

vyf = 19.289 m/s

vxf = vxi

vxf = 8 x cos(35)

vxf = 6.55 m/s

Resultant speed = √(19.289² + 6.55²) = 20.37 m/s

Magnitude of the force exerted by the seat on the person

F = ma

F = 65 x 3.9

F = 253.5 N

Since the motion is horizontal, the angle of the motion is zero.

Fx = 253.5cos(0) = 253.5 N

Fy = 253.5sin(0) = 0 N

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