Question

Projectile Motion: If you launch projectile horizontally and drop a stone at the same time from the same height, which one will strike the ground first. Explain why. Assume no air resistance. (Hint: they actually will hit the ground at the same time. HMMM... why?)

Projectile Motion: If you launch a cannon at 15 degrees above horizontal, and another cannon at 75 degrees above horizontal, which one will reach farther horizontal range? Explain your answer.

Answer 1

Hi,

Hope you are doing well.

PART 1:

Bothe the stone and the projectile will reach the ground at the same time.

REASON:

We know that for a half projectile motion, Time of flight is given by,

Where,

is the height above the ground (m).

is acceleration due to gravity (m/s²).

From the above equation, it is clear that the time of flight of projectile only depends on height at which the projectile is launched and acceleration due to gravity and time of flight is independent of horizontal velocity.

Since the stone and projectile is launched from the same height, their time of flight will be the same and they will hit the ground at the same time.

PART 2:

The projectile launched with greater initial speed will reach farther horizontal range.

REASON:

We know that for a projectile motion, horizontal range is given by,

Where,

is the initial horizontal speed (m/s).

is the angle of projectile.

is acceleration due to gravity (m/s²).

In both cases, sin values of the angle will be the same.

In this case, The horizontal range will only depends on initial horizontal speed (). So The projectile launched with greater initial speed will reach farther horizontal range.

Hope this helped for your studies. Keep learning. Have a good day.

Feel free to clear any doubts at the comment section.

Please don't forget to give a thumbs up.

Thank you. :)