Question

Assume we’re able to travel to your planet and decide to take some fireworks with us to celebrate our journey.

During a fireworks display like the one illustrated, a shell is shot into the air with an initial speed of 70.0 m/s at an angle of 75° above the horizontal. The fuse is timed to ignite the shell just as it reaches its highest point above the ground.
Use the acceleration due to gravity (free-fall acceleration) that was calculated for your planet on Step 1 to answer the questions below.
We will have to ignore air resistance on this planet, just like we do for our physics examples on Earth.
What is the horizontal displacement (in meters) of the shell when it explodes?

Answer 1

The horizontal distance covered by the firework will be
`(1876.8)/(g)`

Step-by-step explanation:

Let acceleration due to gravity on the planet be g, initial velocity of the firework be u and angle made with the horizontal be ∅.

writing equation of motion in vertical direction:

`v_(y)=u_(y)+(-g) t`

`u_(y)= u\sin \phi`

and
`v_(y)=0`

therefore
`(u\sin \phi )/(g) =t`

writing equation of motion in horizontal direction:

`s_(x)=u_(x)t`

`u_(x) = u\cos \phi`

therefore the equation becomes
`s_(x)=(u^(2)   \sin \phi  \cos \phi)/(g)`

therefore horizontal distance traveled =
`(u^(2)\sin 2\alpha \phi )/(2g)=(1876.8)/(g)(m)/(s)`