A Ball Is Thrown Vertically Upward At 10m/S. How High Will It Get, How Long Will It Be In The Air, And How Fast Will It Be Moving When It Hits The Gro

A ball is thrown vertically upward at 10m/s. How high will it get, how long will it be in the air, and how fast will it be moving when it hits the ground?

 

Step 1: Write the given

  1. Initial velocity (upward)= 10 m/s

Step 2: Determine the formula/s that may be utilized

For upward direction:

  1. v(t)=v_{0} - gt
  2. y(t)=y_{0} + v_{0}t-\frac{1}{2}gt^{2}
  3. v(t)^{2}=v_{0}^{2} - 2g(y(t)-y_{0})

For downward direction:

  1. v(t)=v_{0} + gt
  2. y(t)=y_{0} + v_{0}t+\frac{1}{2}gt^{2}
  3. v(t)^{2}=v_{0}^{2} + 2g(y(t)-y_{0})

Step 3: Find the maximum height of the ball

  1. Use the eq 3 for upward direction
  2. In order to find hte max height, use 0 m/s as the final velocity
  3. (0 m/s)²=(10 m/s)²-2(9.81 m/s²)(max height)
  4. 10²=2*9.81*max height
  5. The maximum height of the ball will reach is 5.10 meters.

Step 4: Find the time it will stay in the air

  1. For upward motion, use equation 1
  2. 0 m/s= 10 m/s-(9.81 m/s²)(t upward)
  3. The time it will take to reach the maximum height is 1.02 sec.
  4. For downward motion, use equation 2
  5. 5.10 meters=(0 m/s)(t downward)+(1/2)(9.81 m/s²)(t downward)²
  6. The time it will take to reach the ground from maximum height is also 1.02 sec.
  7. The total time the ball will be in the air is 2.04 sec.

Step 5: Find the velocity of the ball when it hits the ground

  1. Use eq 3 for downward motion
  2. (final velocity)²=(0 m/s)²+(2)(9.81 m/s²)(5.10 m)
  3. The velocity of the ball when it hit the ground is equal to 10 m/s.

Answers:

  • Maximum height is equal to 5.10 m
  • Time of the ball in the air is 2.04 sec
  • Velocity of ball when it hits the ground is 10 m/s

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