Question

A cannon can make a maximum angle of 30 degrees with the horizon. What is the minimum speed of a cannon ball if it must clear a 10-m-high obstacle 30 m away?

1. 28.3 m/s
2. 30.5 m/s
3. 32.8 m/s
4. 34.1 m/s
5. 36.8 m/s

Answer 1

28.3 m/s

Step-by-step explanation:

From the question given above, the following data were obtained:

Angle of projection (θ) = 30°

Maximum height (H) = 10 m

Acceleration due to gravity (g) = 10 m/s²

Initial velocity (u) =?

Thus, we can obtain the minimum velocity cannon ball by using the following formula:

H = u²Sine² θ / 2g

10 = u² × (Sine 30)² / 2× 10

10 = u² × (0.5)² / 20

10 = u² × 0.25 / 20

10 = u² × 0.0125

Divide both side by 0.0125

u² = 10/ 0.0125

u² = 800

Take the square root of both side

u = √800

u = 28.3 m/s

Therefore, the minimum speed of the cannon ball is 28.3 m/s