How is it possible a plant can sustain itself for 70 years locked inside a jar?
1 answer:
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a) 2.75 s
The vertical position of the ball at time t is given by the equation
where
h = 4 m is the initial height of the ball
u = 12 m/s is the initial velocity of the ball (upward)
g = 9.8 m/s^2 is the acceleration of gravity (downward)
We can find the time t at which the ball reaches the ground by substituting y=0 into the equation:
This is a second-order equation. By solving it for t, we find:
t = -0.30 s
t = 2.75 s
The first solution is negative, so we discard it; the second solution, t = 2.75 s, is the one we are looking for.
b) -15.0 m/s (downward)
The final velocity of the ball can be calculated by using the equation:
where
u = 12 m/s is the initial (upward) velocity
g = 9.8 m/s^2 is the acceleration of gravity (downward)
t is the time
By subsisuting t = 2.75 s, we find the velocity of the ball as it reaches the ground:
And the negative sign means the direction is downward.
a) 10.5 m/s
While for observer 1, in motion with the car, the ball falls down straight vertically, according to observer 2, which is at rest, the ball is also moving with a horizontal speed of:
As the ball falls down, it also gains speed along the vertical direction (due to the effect of gravity). The vertical speed is given by
where
is the initial vertical speed
g = 9.8 m/s^2 is the acceleration of gravity
t is the time
Therefore, after t = 1.00 s, the vertical speed is
And so the speed of the ball, as observed by observer 2 at rest, is given by the resultant of the horizontal and vertical speed:
b)
As we discussed in previous part, according to observer 2 the ball is travelling both horizontally and vertically.
The direction of travel of the ball, according to observer 2, is given by
We have to understand in which direction is this angle measured. In fact, the car is moving forward, so has forward direction (we can say it is positive if we take forward as positive direction).
Also, the ball is moving downward, so is negative (assuming upward is the positive direction). This means that the direction of the ball is forward-downward, so the angle above is measured as angle below the positive horizontal direction: