A ball is thrown with speed of 29.4m/s at an angle of 30 o above the horizontal. The total time taken to cover the horizontal range is:a.8sb.3sc.4sd.6s
Question
A ball is thrown with speed of 29.4 m/s at an angle of 30° above the horizontal. The total time taken to cover the horizontal range is:
- a. 8s
- b. 3s
- c. 4s
- d. 6s
Solution
The total time of flight for a projectile launched at an angle θ with an initial speed v is given by the formula:
t = 2v*sin(θ) / g
where: v = initial speed θ = launch angle g = acceleration due to gravity (approximately 9.8 m/s²)
First, we need to convert the launch angle from degrees to radians. In radians, 30 degrees is equivalent to π/6.
Then we can plug in the given values:
t = 229.4 m/ssin(π/6) / 9.8 m/s² t = 58.8 m/s * 0.5 / 9.8 m/s² t = 29.4 m / 9.8 s² t = 3 s
Therefore, the total time taken to cover the horizontal range is 3 seconds.
The correct answer is:
b. 3s
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