Projectile Motion on a Ramp: Solving for Distance, Time, and Velocity

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A toy car is driven off a ramp at a speed of 3.26 m/s and an angle of 34.7 degrees. To determine how far the car travels horizontally before landing, the problem requires applying standard kinematics equations for both horizontal and vertical motion. By analyzing the relationship between horizontal distance and vertical height using the ramp's angle, one can eliminate variables to solve for time in the air and final velocity before landing. The discussion emphasizes the importance of breaking down the motion into horizontal and vertical components to apply the correct formulas. Understanding these principles is crucial for solving projectile motion problems effectively.
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Homework Statement


A toy car is driven horizontally off of a level platform at the top of a ramp as shown. The velocity of the car just as it leaves the ramp is 3.26 m/s. The angle of the ramp with respect to the horizontal direction, theta, is 34.7 °.

How far does the car travel horizontally before landing on the ramp?
How long is the car in the air?
What is the magnitude of the car's velocity just before it lands on the ramp?


Homework Equations


Standard kinematics equations.
 

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Nearly all 2D motion problems can be solved by this method:
Make two headings for "horizontal" and "vertical".
In each case, ask yourself what kind of motion is involved and write down the basic formulas for the motion. You should have one formula for horizontal and two (one v= and one d= ) for the vertical.
Fill in the numbers you know in all three formulas.
In this case, you also have a relationship between y and x when the car touches the ramp because of the straight ramp at a known angle. Use that to eliminate y or x in the three formulas.
Now you should be able to solve one of the formulas and find something, hopefully time of touching down.
 
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Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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