For which value of theta is the range of a projectile fired from ground level a maximum?

Question

a. 30 degrees above the horizontal.
b. 45 degrees above the horizontal.
c. 60 degrees above the horizontal.
d. 90 degrees above the horizontal.

Please explain, thanks!

Answer 1

Projectile range would be the equivalent of horizontal distance.
The forces involved are gravity (acting on the projectile's mass in the vertical direction), and the "push" from the initial thrust.

As the angle of the firing position increases above the horizontal, more of the initial push is used to combat gravity.

If the angle is too low, the projectile will meet the ground before it's maximum range (not enough action against gravity).

For most projectiles, the optimum angle is between 42 and 45 degrees (depending on the strength of the initial impetus). This is because the trajectory approximates a parabola.

With the given choices, the answer will have to be 45 degrees (answer B)...

Answer 2

b. 45 degrees above the horizontal.

Answer 3

b

Just do the calculations with the same object at the same force, but with different angles.