Question

1.An object falls from rest on a high tower and takes 5.0 s to hit the ground. Calculate the object’s position from the top of the tower at 1.0 s intervals. Make a position-time graph for the object’s motion. In your response, show what you are given, the equation that you used, any algebra required, a table of data, and your graph.

g = 9.8 m/s2

Answer 1

Position of ball from top of tower after 1 second is 4.9 m

Position of ball:
`y=-4.9t^2+122.5`

Explanation:

An object falls from rest on a high tower and takes 5.0 s to hit the ground.

• Initial speed, u = 0

• Height of tower,
  `h_0`

• Acceleration due to gravity,
  `g=9.8\ m/s^2`

Let position of object from top of tower be y

Using formula, v =u - gt

`v=0-9.8* 5`

`v=49\ m/s`

Speed of object when hit the ground.

Height of tower, H₀

`H_0=(49^2-0)/(2* 9.8)=122.5\ m`

Velocity of ball after 1 s

`v=0-9.8* 1`

`v=-9.8\ m/s`

Using formula,
`s=(v^2-u^2)/(2g)`

`y=(9.8^2-0^2)/(2* 9.8)`

`y=4.9\ m` From top of tower

Now find position of ball from top of tower.

`y=-(1)/(2)* 9.8* t^2+122.5`

`y=-4.9t^2+122.5`

Please find the attachment for graph.

Answer 2

We will be using this equation for this problem
d = ut + ½.at²
Given:
initial velocity, u = 0 (falling from rest)
acceleration, a = +9.80 m/s²(taking down as the convenient positive direction)
Time = 1.0s, 2.0s, 3.0s, 4.0s, 5.0s

Using .. d = ½.at² each time (each calculation is the distance from the top)
For 1.0s .. d = ½ x 9.80 x (1²) = 4.90 m
For 2.0s .. d = ½ x 9.80 x (2²) = 19.60 m
3.0s .. d = 44.10m (you show the working for the rest)
4.0s .. d = 78.40 m
5.0s .. d = 122.50m

Plot distance (displacement from the top) on the y-axis against time on the x-axis (label axes and give units for each).The line of best fit will be a smoothly upward curving line getting progressively steeper. Do not join graph points with straight lines.