PhysicsBowl 2017 Q32

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PhysicsBowl 2017

32) This question gives us the initial speed and direction of a projectile and asks us to find out the time when a projectile makes a 20-degree angle with its original position. We can start by drawing out the situation.

Where v is velocity, x is displacement in x-direction, and y is displacement in y-direction

Next, we can relate x to y with the tangent trigonometry function.

Where x is displacement in x-direction, and y is displacement in y-direction

Using kinematics we can come up with a relation between x, y, and time. Remember that there is only acceleration in the y-direction.

Where d is displacement, v[o] is initial velocity, t is time, a is acceleration, x is displacement in x-direction, and y is displacement in y-direction, θ[i] is initial launch angle, and g is acceleration due to gravity

Finally, by plugging this into our equation for tan(20°), we can come up with an equation where time is the only unknown.

Where v[o] is initial velocity, θ[i] is the launch angle, t is time, and g is acceleration due to gravity

Answer: C