Finding max. distance and time (projectile motion)

[cvc121]

Homework Statement

John plans to drive a car off of one ramp and land on a similar opposing ramp. The ramps are slanted at 30 degrees. His car leaves one ramp at a speed of 30m/s.

a) What is the maximum distance between the ramps for the stunt to succeed?
b) How much time does the car spend in the between ramps?

Homework Equations

The Attempt at a Solution

My attempt at the solution is shown below. Can anyone verify my work and see if I am on the right track? Note: I did question b) first because I needed that time value for a). Thanks. All help is very much appreciated!

 

[SteamKing]

Homework Statement

John plans to drive a car off of one ramp and land on a similar opposing ramp. The ramps are slanted at 30 degrees. His car leaves one ramp at a speed of 30m/s.

a) What is the maximum distance between the ramps for the stunt to succeed?
b) How much time does the car spend in the between ramps?

Homework Equations

The Attempt at a Solution

My attempt at the solution is shown below. Can anyone verify my work and see if I am on the right track? Note: I did question b) first because I needed that time value for a). Thanks. All help is very much appreciated!

The distance between ramps will not be measured in m/s.