2. A long jumper leaves the ground with an initial speed of 12 m/s at an angle o

Question

2. A long jumper leaves the ground with an initial speed of 12 m/s at an angle of 28-degrees above the horizontal. The jumper lands in some sand at the same height as where they jumped from. a. Find the maximum height it can reach. b. Find the total time required before it lands. c. Find the range of the ball (aka how far it moves horizontally). d. Find the horizontal and vertical components of the final velocity vector. e. Find the final speed and the angle that the ball strikes the ground with.

Explanation / Answer

According to the given problem,

a) The maximum height ,

Hmax = u2Sin2 /2g

= 1.62m

b) The total time of flight,

t = 2usin /g

t = 1.15 s

c) The range of the ball,

R = u2sin2 /g

= 12.17 m

d)The horizontal component of final velocity,

vx = ux = ucos = 10.6m/s

The vertical component of velocity,

vy = uy - gt = usin - gt = -5.65 m/s

e) the final speed,

v = 12 m/s

The angle is ,

' = -28o

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