Question

Projectile Motion : Show that a ball thrown at an angle of 60 degrees will go three times as high as at an elevation of 30 degrees but travel the dame horizontal distance. The initial speed is the same at both angles.

Answer 1

Max height of projectile = u²sin²/2g

Horizontal range = u²sin2/g

Case 1 = = 60^o

H = u²sin²/2g

H₁ = u²sin²60/2g

H₁ = (0.75*u²)/2g..........................eq1

case 2 = = 30^o

H₂ = u²sin²30/2g

H₂ = (0.25*u²)/2g..........................eq2

compare eq1 with eq2

H₁ = 3H₂

For horizontal range

Case 1 = = 60^o

R₁ = u²sin2/g

R₁ = u²sin120/g

R₁ = 0.866*u²/g....................eq3

Case 2 = = 30^o

R₂ = u²sin2/g

R₂ = u²sin60/g

R₂ = 0.866*u²/g..........................eq4

compare eq3 and eq4

R₁ =R₂