Question

a stone is thrown up with a velocity 29.4 m/s at an angle of 30° with a horizontal. find the total time of flight maximum height reached and the horizontal range cover​

Answer 1

Answer :

• Time of flight of stairs stone is 2.94 s.
• Maximum height reached by the stone is 10.8 m.
• Horizontal covered by the stone is 74.86 m

Explanation :

Given :

• Initial velocity of the stone, u = 29.4 m/s
• Acceleration due to gravity, g = 10 m/s²
• Angle of Projection, θ = 30°

To find :

• Time of flight of stairs stone, t = ?
• Maximum height reached by the stone, h = ?
• Horizontal covered by the stone, x = ?

Knowledge required :

Formula for time of flight in case of a projectile :

⠀⠀⠀⠀⠀⠀⠀⠀⠀t = (2u sinθ)/g

Where,

• t = Time of flight
• u = Initial velocity
• θ = Angle of projection
• g = Acceleration due to gravity

Formula for maximum height reached by a body in case of a projectile :

⠀⠀⠀⠀⠀⠀⠀⠀⠀h = (u² sin²θ)/2g

Where,

• h = Maximum height
• u = Initial velocity
• θ = Angle of projection
• g = Acceleration due to gravity

Formula for horizontal range in case of a projectile :

⠀⠀⠀⠀⠀⠀⠀⠀⠀x = (u² sin2θ)/g

Solution :

To find the total time taken by the stone :

By using the formula for time of flight and substituting the values in it, we get :

⠀⠀=> t = (2u sinθ)/g

⠀⠀=> t = (2 × 29.4 × sin30°)/10

⠀⠀=> t = (2 × 29.4 × ½)/10 [sin30° = ½]

⠀⠀=> t = 29.4/10

⠀⠀=> t = 2.94

⠀⠀⠀⠀⠀⠀⠀∴ t = 2.94 s

To find the maximum hieght reached by the stone :

By using the formula for maximum height in case of a projectile and substituting the values in it, we get :

⠀⠀=> h = (u² sin²θ)/2g

⠀⠀=> h = (29.4² × sin²30°)/(2 × 10)

⠀⠀=> h = (864.36 × 1/2²)/20

⠀⠀=> h = (864.36 × 1/4)/20

⠀⠀=> h = 216.09/20

⠀⠀=> h = 10.8 (approx.)

⠀⠀⠀⠀⠀⠀⠀∴ h = 10.8 m

To find the horizontal range of the stone :

By using the formula for horizontal range in case of a projectile and substituting the values in it, we get :

⠀⠀=> x = (u² sin2θ)/g

⠀⠀=> x = (29.4² × sin2(30°))/10

⠀⠀=> x = (29.4² × sin60°)/10

⠀⠀=> x = (864.36 × √3/2)/10 [sin60° = √3/2]

⠀⠀=> x = (432.18 × √3)/10

⠀⠀=> x = (432.18 × √3)/10

⠀⠀=> x = 748.56(approx.)/10

⠀⠀=> x = 74.86

⠀⠀⠀⠀⠀⠀⠀∴ x = 74.86 m

Therefore,

• Time of flight of stairs stone, t = 2.94 s
• Maximum height reached by the stone, h = 10.8 m
• Horizontal covered by the stone, x = 74.86 m.