A ball is thrown straight up with enough speed so that it is in the air for several seconds. Assume the positive direction is upwards. What is its velocity 1.5s before it reaches its highest point?What is the change in its velocity, v, during this 1.5-s interval? What is its velocity 1.5s after it reaches its highest point?What is the change in velocity, v, during this 1.5-s interval?
the ball is uniformly accelerated by gravitational force
the velocity is zero at the peak
1.5 s before the peak, the velocity is
... 1.5 * g upward
1.5 s after the peak, the velocity is
... 1.5 * g downward
To determine the velocity of the ball at various points in its trajectory, we need to consider its motion and the effects of gravity. We can break down the problem into three phases: upward motion, at the highest point, and downward motion.
1. Upward Motion:
When the ball is thrown straight up, it accelerates due to the force of gravity acting in the downward direction. The initial velocity at the start of the upward motion is positive (upwards). As the ball moves upwards, its velocity decreases until it reaches its highest point.
To find the velocity 1.5 seconds before it reaches the highest point, you would need to know the initial velocity of the ball. Without that information, we cannot determine the exact value. However, we can analyze the direction of velocity. Since the ball is in the upward phase, the velocity at any given time will be positive. Therefore, the velocity 1.5 seconds before reaching the highest point will still be positive.
2. At the Highest Point:
At the highest point of its trajectory, the ball's velocity momentarily becomes zero. This occurs because the upward motion stops and the ball reaches its maximum height. Therefore, the velocity at the highest point is zero.
3. Downward Motion:
After reaching the highest point, the ball starts moving downward. Its velocity gradually increases as the force of gravity accelerates it in the downward direction. Similar to the upward motion, we need to know the initial velocity to determine the exact value of the velocity 1.5 seconds after reaching the highest point. However, we can determine the direction of the velocity. Since the ball is in the downward phase, the velocity will be negative (downwards).
Regarding the change in velocity during the given 1.5-second intervals:
- In the first 1.5 seconds (upward phase), the velocity decreases as the ball moves against the force of gravity. The change in velocity during this interval will be negative.
- At the highest point (no motion), there is no change in velocity, so the change in velocity (delta v) is zero.
- In the next 1.5 seconds (downward phase), as gravity accelerates the ball downwards, the velocity increases in the downward direction. The change in velocity during this interval will be positive (assuming the ball was initially thrown upwards with enough speed).