Physics 2d kinematics, projectile motion

[vankyy]

Homework Statement

Dr. Evil runs out to his car which is parked at the bottom of a hill that is inclined with the horizontal at 20(degrees) and blasts up the hill at an acceleration of 6 m/s2. James Bond runs out behind Dr. Evil to a mortar that is located conveniently exactly where Dr. Evil’s car was parked. The mortar is aimed up the hill and elevated at an angle of 60(degrees) with the horizontal and fires a projectile with an initial velocity of 50 m/s. How much time passes after Dr. Evil starts does James fire the mortar if he successfully ends Dr. Evil’s career in crime?

Can you guys help me with this question. I do not need you guys to do my homework just push me towards the right path. Any help is appreciated, thank you.

 

[PeterO]

Homework Statement

Dr. Evil runs out to his car which is parked at the bottom of a hill that is inclined with the horizontal at 20(degrees) and blasts up the hill at an acceleration of 6 m/s2. James Bond runs out behind Dr. Evil to a mortar that is located conveniently exactly where Dr. Evil’s car was parked. The mortar is aimed up the hill and elevated at an angle of 60(degrees) with the horizontal and fires a projectile with an initial velocity of 50 m/s. How much time passes after Dr. Evil starts does James fire the mortar if he successfully ends Dr. Evil’s career in crime?

Can you guys help me with this question. I do not need you guys to do my homework just push me towards the right path. Any help is appreciated, thank you.

First thing - draw a picture.

An endless slope up at 20 degrees.

Now add the mortar - an inverted parabola starting up at 60 degrees [it is just a sketch so you don't have to get it exact, but please get it close to 20 & 60 degrees]

You will see the parabola intersects the slope further up the slope.

Using projectile motion analysis, you can find when the mortar will land, and how far away it is, and how.

You want the evil doctor to be there when the mortar comes down.

Given his acceleration you can calculate when he will get there.

Lets suppose the mortar takes 10 seconds to get there, and the Dr takes 15 seconds to get there, then JB should fire 5 seconds after the doctor leaves.

As a trial run, you might like to work the problem on flat ground - as it is easier to work the projectile in that case, before getting into the real problem.

 

[zaper]

The first thing that I would recognize here is that the mortar is in the air for a set amount of time and will go a set distance. If you can figure out the time that it takes to hit and the distance it travels in that time then you can find how far Dr. Evil went when it hit him

 

[vankyy]

Thank you for your time guys. I have the sketch and I got the main idea, the thing that I cannot understand is, how do I figure out the time it takes for the mortar to hit the ground, if I do not know where it is going to land (how far above the ground)? If delta "y" was it would be no problem, but since the car is going up in 20 degrees, depending on the time delta "y" would be different. Thank you one more time.

 

[PeterO]

Thank you for your time guys. I have the sketch and I got the main idea, the thing that I cannot understand is, how do I figure out the time it takes for the mortar to hit the ground, if I do not know where it is going to land (how far above the ground)? If delta "y" was it would be no problem, but since the car is going up in 20 degrees, depending on the time delta "y" would be different. Thank you one more time.

You could draw standard cartesian [x-y] axes with the origin at the start point.

The eqaution of the hill is then y = tan(20).x [like a y = 2x line, but not as steep]

The parabola has equation of the form y = ax(x-b), where b is how far away the projectile would land on flat ground, and a is the scale factor to get the projectile to the correct maximum height.

Solving those two equations simultaneously will give the the point of intersection.

From that you can work out how far above the starting point the final explosion takes place.

 

[vankyy]

@PeterO thank you so much for your help! I got 6.98s for the mortar and 7.86s for the Dr. so it turns out, the mortar needs to be fired 0.7s after the Dr. leaves. I really hope this is correct :). Thank you!