The velocity of a diver just before hitting the water is -8.7 m/s, where the minus sign indicates that her motion is directly downward. What is her displacement during the last 0.98 s of the dive?
To find the displacement during the last 0.98 s of the dive, we need to use the equation for displacement, which is given by:
displacement = initial velocity * time + (1/2) * acceleration * time^2
Given:
Initial velocity (u) = -8.7 m/s (negative sign indicates downward motion)
Time (t) = 0.98 s
Since the question does not provide information about acceleration, we can assume the acceleration during free fall due to gravity is approximately -9.8 m/s^2.
Using the equation for displacement:
displacement = (-8.7 m/s) * (0.98 s) + (1/2) * (-9.8 m/s^2) * (0.98 s)^2
Calculating this expression:
displacement = -8.526 m + (-4.8084 m)
Simplifying:
displacement ≈ -13.33 m
Therefore, the diver's displacement during the last 0.98 s of the dive is approximately -13.33 meters.
To determine the displacement of the diver, we need to use the equation of motion:
displacement = initial velocity * time + (0.5 * acceleration * time^2)
Given the velocity of the diver just before hitting the water as -8.7 m/s, we can assume this as the initial velocity. Here, the negative sign indicates that the motion is directly downward.
Since the question asks for the displacement during the last 0.98 seconds of the dive, we can assume this as the time, t = 0.98s.
However, we do not have the value of acceleration, so this needs to be calculated first.
Since the diver is moving vertically downward, we can assume the acceleration due to gravity as the value of acceleration, which is approximately 9.8 m/s^2. But since the motion is already given as -8.7 m/s in the downward direction, we will consider the acceleration as negative.
Plug the values into the equation:
displacement = (-8.7 m/s) * (0.98 s) + (0.5 * (-9.8 m/s^2) * (0.98 s)^2)
Now we can calculate the displacement.
With an acceleration of gravity of 9.8 m/s^2, the velocity 0.98s earlier was
-8.7 + 9.6 = +0.9 m/s. (It must have been a springboard drive).
The average velocity was -3.9 m/s.
The vertical displacement during the previous 0.98 s was
-3.9 x 0.98 = -3.8 m