Atrack star in the long jump goes into the jump at 12 m/s and launches herself at 20.0 degrees above the horizontal. what is the magnitude of her horizontal displacement?
a. 4.6 m
b. 9.2 m
c. 13 m
d. 15 m

Explanation:

1. Break down the velocity into its horizontal and vertical components

2. Calculate the time of flight

Use the vertical component of velocity to calculate the time to the height of the jump.

It will take the same time to reach the ground.

Thus,

Time of flight = 2t = 2 × 0.419 s  = 0.837 s

3. Calculate the horizontal distance

s = vt = 11.3 m·s⁻¹ × 0.837 s = 9.4 m  

b. 9.2m

Explanation:

Vertical component of velocity:

12sin20

a = -9.8

t for max height

0 = 12sin20 - 9.8t

t = 0.4188001755

Time of the journey:

2t = 0.837600351

Horizontal component of velocity:

12cos20

Horizontal displacement:

(12cos20)(0.837600351)

9.445042428 m