A Sky-diver(falling vertically)starts from rest at time t=0.His acceleration is non-uniform until be reaches a steady speed of 50m/s at t=10s.He open his parachute at t=20s and decelerates until t=25s.From t=25s he falls at a steady speed of 5m/s.Draw the speed-time graph for the sky-diver
To draw the speed-time graph for the skydiver, we need to break down the different stages and calculate the speed at different time intervals.
Stage 1: Time 0s to 10s
During this stage, the skydiver is accelerating and reaches a steady speed of 50 m/s at t=10s. To find the acceleration during this stage, we can use the equation of motion:
v = u + at
Where:
v = final velocity (50 m/s)
u = initial velocity (0 m/s)
a = acceleration
t = time (10s)
Substituting the known values, the equation becomes:
50 = 0 + a * 10
Simplifying the equation:
50 = 10a
So, the acceleration during stage 1 is 5 m/s^2.
Stage 2: Time 10s to 20s
During this stage, the skydiver maintains a constant speed of 50 m/s. Therefore, the speed remains constant at 50 m/s.
Stage 3: Time 20s to 25s
At time t=20s, the skydiver opens their parachute and starts decelerating until t=25s. Let's assume the deceleration is constant during this stage. Using the same equation of motion:
v = u + at
Where:
v = final velocity (5 m/s)
u = initial velocity (50 m/s)
a = deceleration
t = time (25s - 20s = 5s)
Substituting the known values:
5 = 50 + a * 5
Simplifying the equation:
5 = 50 - 5a
Rearranging the equation:
5a = 50 - 5
5a = 45
So, the deceleration during stage 3 is -9 m/s^2 (note the negative sign indicates deceleration).
Stage 4: Time 25s onwards
After t=25s, the skydiver falls at a steady speed of 5 m/s. Therefore, the speed remains constant at 5 m/s.
Based on these stages, we can now draw the speed-time graph:
|
50 |
| - |
| - |
| - |
| - |
| - |
5 | |----
0 10 20 25
The graph shows the initial acceleration from 0 to 50 m/s in the first 10 seconds, followed by a constant speed of 50 m/s until 20 seconds. At 20 seconds, there is a sudden drop to 5 m/s, indicating the deployment of the parachute. From 25 seconds onwards, the speed remains constant at 5 m/s until the end.
Note: The graph is a simplified representation and may not accurately depict the exact scale of time or speed.
To draw the speed-time graph for the sky-diver, we need to consider the different phases of the sky-diver's motion:
1. From t=0s to t=10s: The sky-diver is accelerating and reaches a steady speed of 50 m/s at t=10s.
2. From t=10s to t=20s: The sky-diver continues to fall at a constant speed of 50 m/s.
3. From t=20s to t=25s: The sky-diver opens his parachute and decelerates.
4. From t=25s onwards: The sky-diver falls at a steady speed of 5 m/s.
Now, let's plot these phases on a speed-time graph:
^
50 | ______
| \
| /
| /
| /
|______/
| \
5 |________\
|
|_________________________
0 10 20 25 t
The graph shows the time (t) on the x-axis and the speed (v) on the y-axis. The sky-diver's speed gradually increases until it reaches 50 m/s at t=10s. From t=10s to t=20s, the speed remains constant at 50 m/s. At t=20s, the sky-diver opens his parachute and starts to decelerate. The deceleration is not specified, so we would need more information to accurately plot this part of the graph. However, we can assume a linear deceleration for simplicity. From t=25s onwards, the sky-diver falls at a steady speed of 5 m/s, as mentioned.
Please note that this graph is a simplified representation, and the exact shape of the graph will depend on the specific acceleration and deceleration values given for the sky-diver's motion.