# Projectile motion problem

#### kprink24

A 5kg object sits at the top of a hemispherical dome (no friction) with a diameter of 96m. A breeze causes the object to start sliding down the dome.

a. Using the object as a projectile, find the hang time
b. Find the horizontal component of the velocity of the projectile
c. Find the distance the object lands from the dome.

Honestly I really don't know where to begin with this problem; on a previous attempt of the problem using different numbers I used a relationship between potential and kinetic energy, but I was unable to find a suitable answer. Even some help finding the equation of the height would be very helpful. Sorry there isn't an explicit attempt at the solution. Thanks so much in advance!

#### Pmb

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kprink24 said:
A 5kg object sits at the top of a hemispherical dome (no friction) with a diameter of 96m. A breeze causes the object to start sliding down the dome.

a. Using the object as a projectile, find the hang time
b. Find the horizontal component of the velocity of the projectile
c. Find the distance the object lands from the dome.
What is the hang time?

kprink24 said:
Honestly I really don't know where to begin with this problem; ..
Sure you do. All kidding aside though, draw a diagram of the problem. Label the important coordinates in the problem. Write down a list of the things that you know and the things that you need to determine, i.e. the solution. In this instance you're looking for thang, vx and D = x(thang) assuming that thang is the time at which the ball hits the ground.

Once you do that the equation that you're looking for will appear ... I hope. #### MBW

Work out an equation for the component of gravity tangential to the surface of dome.
This is the acceleration of the object.
(The component of acceleration perpendicular to the surface of the dome must of course be zero).
From this you can work out an equation for the motion of the object.

At some point I am guessing that the natural parabolic curve describing the continuing path of the object, given its current velocity at that point, will leave the surface of the dome.
(does this have anything to do with to this unfamiliar term "hang time")?