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

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.

isyllus isyllus · Answer 2 · 2025-04-01T11:12:52-04:00

Answer:

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

Position of ball: [tex]y=-4.9t^2+122.5[/tex]

Step-by-step 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, [tex]h_0[/tex]

Acceleration due to gravity, [tex]g=9.8\ m/s^2[/tex]

Let position of object from top of tower be y

Using formula, v =u - gt

[tex]v=0-9.8\times 5[/tex]

[tex]v=49\ m/s[/tex]

Speed of object when hit the ground.

Height of tower, H₀

[tex]H_0=\dfrac{49^2-0}{2\times 9.8}=122.5\ m[/tex]

Velocity of ball after 1 s

[tex]v=0-9.8\times 1[/tex]

[tex]v=-9.8\ m/s[/tex]

Using formula, [tex]s=\dfrac{v^2-u^2}{2g}[/tex]

[tex]y=\dfrac{9.8^2-0^2}{2\times 9.8}[/tex]

[tex]y=4.9\ m[/tex] From top of tower

Now find position of ball from top of tower.

[tex]y=-\dfrac{1}{2}\times 9.8\times t^2+122.5[/tex]

[tex]y=-4.9t^2+122.5[/tex]

Please find the attachment for graph.