1. The problem statement, all variables and given/known data
You throw a ball at a coconut on a stand 4.0 m in front of you and 1.0 m above the point at which you release the ball. If you throw the ball at 10.0 m/s, at what angle(s) should you throw it? How long is the ball in the air in each case?
2. Relevant equations
##v=v_o + at \\ x=x_o + v_o t + \dfrac{1}{2}at^2 ##
3. The attempt at a solution
I am given the horizontal distance (4.0m), vertical distance (1.0m), and the horizontal initial velocity (10.0m/s). I am looking for the angle θ. I have looked over some videos online and I know that there should be two angles where I can hit the coconut (they are complementary angles). I have trouble finding the angle θ because there are two unknowns in my equation (t and θ). I have split the problem into x and y components.
##v_x = v_ox \\ x = x_o + v_o t \\ v_y = v_oy + a_y t \\ y = y_o + y_o t + \dfrac{1}{2}a_y t^2##
I also used ##v_ox = v_o cosθ \\ v_oy = v_o sinθ## and substituted into the original equations. I have tried to cancel out t and solve for θ but I end up with a equation that involves the tangent and cosine function which I don't think is correct. Is this the correct approach to solving this problem?
You throw a ball at a coconut on a stand 4.0 m in front of you and 1.0 m above the point at which you release the ball. If you throw the ball at 10.0 m/s, at what angle(s) should you throw it? How long is the ball in the air in each case?
2. Relevant equations
##v=v_o + at \\ x=x_o + v_o t + \dfrac{1}{2}at^2 ##
3. The attempt at a solution
I am given the horizontal distance (4.0m), vertical distance (1.0m), and the horizontal initial velocity (10.0m/s). I am looking for the angle θ. I have looked over some videos online and I know that there should be two angles where I can hit the coconut (they are complementary angles). I have trouble finding the angle θ because there are two unknowns in my equation (t and θ). I have split the problem into x and y components.
##v_x = v_ox \\ x = x_o + v_o t \\ v_y = v_oy + a_y t \\ y = y_o + y_o t + \dfrac{1}{2}a_y t^2##
I also used ##v_ox = v_o cosθ \\ v_oy = v_o sinθ## and substituted into the original equations. I have tried to cancel out t and solve for θ but I end up with a equation that involves the tangent and cosine function which I don't think is correct. Is this the correct approach to solving this problem?
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