Leap River: Solve for Initial Velocity w/o Air Resistance

[ziddy83]

here's the question...ill make it short

a guy wants to leap a river. THe takeoff ramp is inclined at 53 degrees. The river is 40m wide, and the far bank where he is going to land is 15m below the top of the take off ramp. The river itself is 100 m below the ramp. Ignoring air resistance, find initial velocity.

ok so...the Y i would use for this is simple..85m (100m-15m). But..i can't use the quadratic formula to find t, and i have two unknowns since V is not given either. so far the equations I've used I've had 2 unknowns, so...I need a hint or anything to get me in the right directions. Thanks.

 

[Parth Dave]

Well for starters the y-displacement would be -15 m. The land is 15 m below the ramp, so he has to travel 15 m below the ramp. You're right, youre going to two unknowns, but you also have two equations. Use the quadratic equation to solve for t in one of the equations, but now instead of getting a number you will get something that has v in it. Thats ok, just substitute it into the other equation. Now you have a single equation with a single variable. All you have to do is solve. Algebraically, the question can get a bit complicated. Just make sure you don't make any silly mistakes.

 

[wisper]

This is just like your your monkey problem with the exception of wanting to hit the monkey before it hits the ground at a certain Y coordinate you want to land on the ramp at a certain Y coordinate. Does that help or more info needed?

 

[ziddy83]

Yeah, it does help. So basically for one of the equations ill get something like t= v and i can plug that t into the other equation and find v. thanks guys.