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The greatest height to which a man can throw a stone is h.the greatest distance to which he can throw a ball

The greatest height to which a man can throw a stone is h.the greatest distance to which he can throw a ball
 

Grade:11

1 Answers

Arun
25750 Points
5 years ago
Three facts you should already know: 

1. If you propel an object at a given speed V, it reaches its greatest height if you propel it straight up (not at an angle). This is sort of intuitively obvious. 

2. If you propel an object vertically (so that it reaches its maximum height), its initial speed V and height H are related by: 

V² = 2gH (where g = acceleration due to gravity) 

3. If you propel an object at a given speed V and angle θ with respect to the horizontal, it achieves this horizontal range: 

R = V²sin(2θ)/g 

Now, from the equation in #3, it should be obvious that the maximum range is achieved when sin(2θ)=1; that is, when θ=45°. So, let's assume the man throws at 45°, in which case his range is: 

R = V²/g 

This is related to the maximum height by the equation in #2. Substitute: 

R = (2gH)/g 
= 2H 

This means (assuming the man can throw with equal speed in any direction), that his maximum horizontal range is 2 times the maximum height he can thro

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