A parachutist drops freely from an aeroplane which is flying at a heig...
**Solution:**
To find the velocity of the parachutist on reaching the ground, we can use the equations of motion. Let's break down the problem step by step:
**Step 1: Finding the initial velocity**
The parachutist drops freely from the airplane, so initially, his velocity is zero.
**Step 2: Finding the time taken to open the parachute**
The parachutist is in free fall for 10 seconds before the parachute opens. So, the total time of descent is 10 seconds.
**Step 3: Finding the distance traveled during free fall**
During free fall, the parachutist experiences a net retardation or acceleration due to gravity, which we can consider as -2.5 m/s^2 (negative because it opposes the motion). We can use the equation of motion:
distance = initial velocity * time + 0.5 * acceleration * time^2
Since the initial velocity is zero, the equation simplifies to:
distance = 0.5 * acceleration * time^2
Substituting the values, we get:
distance = 0.5 * (-2.5 m/s^2) * (10 s)^2
distance = 0.5 * (-2.5 m/s^2) * 100 s^2
distance = -125 m
The distance traveled during free fall is -125 meters (negative sign indicates downward direction).
**Step 4: Finding the velocity after the parachute opens**
After the parachute opens, the parachutist experiences a reduced net acceleration due to the air resistance. Let's assume this net acceleration is 'a' m/s^2. The parachutist is in free fall for the remaining time (10 seconds - time taken to open the parachute).
Using the same equation of motion as before:
distance = initial velocity * time + 0.5 * acceleration * time^2
Since the initial velocity is zero and the distance traveled is the remaining height of 2495 meters, the equation becomes:
2495 = 0 + 0.5 * a * (10 - time to open parachute)^2
Substituting the values, we have:
2495 = 0.5 * a * (10 - time to open parachute)^2
Now, solving this equation will give us the value of 'a' and subsequently the velocity of the parachutist on reaching the ground.
A parachutist drops freely from an aeroplane which is flying at a heig...
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