If two rocks are thrown with the same velocity but one at an angle of 45 degrees and the other at an angle of 60 degrees to the horizontal, which rock will fall down faster.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The rocks are thrown upwards with the same velocity. One of them is thrown at angle of 45 degrees with the horizontal and the other at an angle of 60 degrees with the horizontal.

For an object thrown with a velocity V and at an angle A with the horizontal the initial velocity can be split into a horizontal component equal to V*cos A and a vertical component equal to V*sin A.

As the object moves, there is a gravitational force of attraction acting vertically downwards on it. This decreases the vertical component of the velocity by an acceleration of g = 9.8 m/s^2. The horizontal component remains constant throughout.

Using the relation v = u + at, where u is the initial velocity of an object, a is the acceleration acting on it and v is the velocity after t seconds we get V' = V*sin A - 9.8*t

At the highest point of a projectile's path the vertical velocity is 0. And a projectile takes the same amount of time going up as it does in coming down.

0 = V*sin A - 9.8*t gives t = V*sin A/9.8

The time taken by the rock to fall down is given by 2*V*sin A/9.8

As sin 60 is greater than sin 45 the rock thrown up at an angle of 60 degrees takes a longer time to fall to the ground.

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