a body thrown with initial speed of 96 feet per second reaches the ground after G is equal to 32 feet per second square
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You can do this by solving simultaneous equations for final position and final velocity, assuming no air resistance, but I don't like to use that approach. It makes the problem look too much like a math problem with little context and doesn't aid conceptual understanding.
I assume you're using 32 ft/s^2 for the acceleration. From this you can quickly determine how long it takes the stone to reach it's highest point. It will lose 32 ft/s of the 40 ft/s in the first second. That leaves 8 ft/s of upward speed. It will take an additional 1/4 s to lose that speed.
It then takes 1.25 s to reach the highest point.
It's average speed while going upward is midway between the starting speed of 40 ft/s and the speed at the top of zero. I.e., average speed = 20 ft/s.
The increase in height is average speed times time or 25 ft.
Now it will fall a total of 225 ft. to the ground from an initial speed of zero. Here it does makes sense to use an equation, but the equation has zero for the initial speed and only needs the falling distance and the known acceleration to find the time.
I assume you're using 32 ft/s^2 for the acceleration. From this you can quickly determine how long it takes the stone to reach it's highest point. It will lose 32 ft/s of the 40 ft/s in the first second. That leaves 8 ft/s of upward speed. It will take an additional 1/4 s to lose that speed.
It then takes 1.25 s to reach the highest point.
It's average speed while going upward is midway between the starting speed of 40 ft/s and the speed at the top of zero. I.e., average speed = 20 ft/s.
The increase in height is average speed times time or 25 ft.
Now it will fall a total of 225 ft. to the ground from an initial speed of zero. Here it does makes sense to use an equation, but the equation has zero for the initial speed and only needs the falling distance and the known acceleration to find the time.
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