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PhysicsBowl 2019 Q11


11) This question asks us to find how the horizontal range of a projectile would change if we double the launch speed of the projectile.


The question tells us that the projectile starts and ends at the same height. Using the conservation of energy, we know that if the projectile starts and ends at the same height, the initial and final velocity in the y-direction will be of the same magnitude and opposite direction. Using this information, we can solve for a general equation for the time it takes for the object to complete its path.

Where m is mass, v is velocity, a is acceleration, t is time, g is acceleration due to gravity, and θ is the angle of elevation of launch

At this point, we have an equation for the time it takes for the ball to hit the ground. Our next step is to calculate the horizontal distance. Since there are no forces acting horizontally on the ball, we know that there is a constant horizontal velocity.

Where R is horizontal range, v is velocity, t is time, θ is angle of elevation of launch, and g is acceleration due to gravity

Now that we have an equation for the horizontal range, we can compare the first and second situations to find how the range is affected.

Where R is horizontal range, v is velocity, θ is angle of elevation of launch, and g is acceleration due to gravity

Answer: D

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