rick shoots a basketball at an angle of 35° from the horizontal. it leaves his hands 7 feet from the ground…
rick shoots a basketball at an angle of 35° from the horizontal. it leaves his hands 7 feet from the ground with a velocity of 20 ft/s. step 1 of 2: construct a set of parametric equations describing the shot. round all final values to the nearest tenth.
Answer
Explanation:
Step1: Find the horizontal component of velocity
The horizontal component of velocity (v_x) is given by (v\cos\theta), where (v = 20) ft/s and (\theta=35^{\circ}). (v_x=20\cos(35^{\circ})\approx20\times0.819\approx16.4) ft/s. The parametric equation for the horizontal position (x(t)) is (x(t)=v_x t), so (x(t)=16.4t).
Step2: Find the vertical component of velocity and initial height
The vertical component of velocity (v_y) is given by (v\sin\theta), where (v = 20) ft/s and (\theta = 35^{\circ}). (v_y=20\sin(35^{\circ})\approx20\times0.574\approx11.5) ft/s. The initial height (y_0 = 7) feet. The parametric equation for the vertical position (y(t)) is (y(t)=- 16t^{2}+v_y t + y_0). Substituting the values, we get (y(t)=-16t^{2}+11.5t + 7).
Answer:
The parametric equations are (x(t)=16.4t) and (y(t)=-16t^{2}+11.5t + 7)