A girl throws a stone from a bridge. Consider the following ways she might throw the stone. The speed of the stone as it leaves her hand is the same in each case.
Case A: Thrown straight up.
Case B: Thrown straight down.
Case C: Thrown out at an angle of 45° above horizontal.
Case D: Thrown straight out horizontally.
In which case will the speed of the stone be greatest when it hits the water below?
In which case will the speed of the stone be greatest when it hits the water below?
The case in which the speed of the stone will be greatest when it hits the water below is Case D: Thrown straight out horizontally.
To determine in which case the speed of the stone will be greatest when it hits the water below, we need to analyze the motion of the stone in each scenario.
Case A: Thrown straight up.
When the stone is thrown straight up, its initial velocity is upwards. As the stone reaches its highest point, its velocity decreases to zero. Then, it starts falling back down due to gravity. The stone hits the water below with a lower speed than the initial velocity.
Case B: Thrown straight down.
In this case, the stone's initial velocity is downwards. It accelerates due to gravity and hits the water with an increasing speed. Therefore, the speed of the stone when it hits the water will be greater than its initial velocity.
Case C: Thrown out at an angle of 45° above horizontal.
When the stone is thrown at an angle of 45° above the horizontal, it has both horizontal and vertical components of velocity. The vertical component increases until it reaches its highest point and then decreases due to the effects of gravity. The horizontal component remains constant. When the stone hits the water, its vertical component will be lower than its initial velocity, but the horizontal component will remain the same. Thus, the speed of the stone when it hits the water will be lower than the initial velocity.
Case D: Thrown straight out horizontally.
In this case, the stone is thrown horizontally, meaning its initial velocity only has a horizontal component. There is no vertical component, so the stone is not affected by gravity in the vertical direction. Therefore, the speed of the stone remains constant throughout its motion. When it hits the water, the speed will be the same as its initial velocity.
Comparing the scenarios, we find that the speed of the stone will be greatest when it is thrown straight down (Case B).
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