A tennis ball projected at an angle 0 attains a range R = 78. If the velocity imparted to the ball by the racket is 30 ms\(^{-1}\), calculate O. [ g = 10 ms...
Question 1 Report
A tennis ball projected at an angle 0 attains a range R = 78. If the velocity imparted to the ball by the racket is 30 ms\(^{-1}\), calculate O. [ g = 10 ms\(^{-2}\)]
Answer Details
Using the range formula. For a projectile launched with speed u at angle \(\theta\), the horizontal range is
\[ R = \frac{u^{2}\sin2\theta}{g} \]With \(R = 78\ \text{m}\), \(u = 30\ \text{m/s}\), \(g = 10\ \text{m/s}^{2}\):
\[ 78 = \frac{30^{2}\sin2\theta}{10} = \frac{900\sin2\theta}{10} = 90\sin2\theta \] \[ \sin2\theta = \frac{78}{90} = 0.867 \] \[ 2\theta = \sin^{-1}(0.867) = 60^{\circ} \quad(\text{or } 120^{\circ}) \] \[ \theta = 30^{\circ} \quad(\text{or } 60^{\circ}) \]The ball is projected at \(\theta \approx \mathbf{30^{\circ}}\) (the complementary angle \(60^{\circ}\) gives the same range).
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