You buy a plastic dart gun, and being a clever physics student
you decide to do a quick calculation to find its maximum
horizontal range.
you shoot the gun straight up, and it takes 4.0 seconds for the
dart to land back at the barrel (ignoring air resistance).
(a) what angle must your fire your gun to reach this max distance?
(b) what is the maximum horizontal range of your dart gun?
(c) what are the components of your initial velocity?

Part a)

Part b)

Part c)

Explanation:

Since it took 4.0 s to come back at the same position so we can say

Part a)

Now we know that horizontal range of projectile is given as

Now this range would be maximum if the angle of the projectile is giving maximum value of sine

so we have

Part b)

For maximum range we have

Part c)

Since we projected at an angle of 45 degree

so the components are given as

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