To calculate the acceleration of the flat car, we can use the equation of motion for an object in free fall:
h = (1/2)gt^2,
where h is the height, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time. Since the plum is at a height of 19.6 m and Sam is 29.4 m away from the point directly under the plum, the total distance Sam needs to close is 19.6 + 29.4 = 49 m.
Using the equation of motion, we can rearrange it to solve for t:
t = sqrt(2h/g).
Plugging in the values, we get:
t = sqrt(2 * 19.6 / 9.8) = sqrt(4) = 2 s.
Therefore, it will take Sam 2 seconds to get directly under the falling plum.
To find the acceleration of the flat car, we can use the formula:
a = (vf - vi) / t,
where vf is the final velocity, vi is the initial velocity (which is 0 since the car is at rest), and t is the time. We know that vf is the distance traveled divided by the time:
vf = (49 m) / (2 s) = 24.5 m/s.
Now we can calculate the acceleration:
a = (24.5 m/s - 0 m/s) / (2 s) = 12.25 m/s^2.
Therefore, Sam needs his flat car to accelerate at a rate of 12.25 m/s^2 in order to catch the plum just before it hits the ground.
Sam while sitting in a flat car at rest notices a plum about to fall from a tall plumb tree. The height of the plum from over the Sam is 19.6 m, and Sam is 29.4 m to get directly under the falling plum. If Sam must catch the plum just before it hits the ground calculate (a) the acceleration of his flat car to get him there quickly, (b) the time it would requires
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