a boy wishes to throw a ball through a house via two small openings, one in the front and the other in back window, the second window being directly behind the first.if the boy stands at the distance of 5m in front 0f the house and the house is 6m deep and if the opening in the front window is 5m above him and that in the back window 2m higher, calculate the velocity and the angle of projection of the ball that will enable him to accomplish his desire.
Answers
Answer:
14.9 m/s
52.5°
Explanation:
A boy wishes to throw a ball through a house via two small openings one in the front and the other in back window the second window being directly behind the first if the boy stand at a distance of 5m in front of the house and the house is 6m deep and if the opening in front window is 5m above him and that in the back window 2m higher Calculate the velocity and angle of projection of the ball that will enable him to accomplish his desire.
If We Understand this Question
The Horizontal Distance = 5 m When Vertical Distance = 5 m
& Horizontal Distance = 5 + 6 = 11m When Vertical Distance = 5+2 = 7 m
Now Let say Velocity = V & angle = α
Horizontal Speed = VCosα
Vertical Speed = VSinα
Let say at T₁ time Ball crosses front window
then Horizontal Distance = VCosα*T₁ = 5 m => T₁ = 5/ VCosα
& Vertical Distance = VSinαT₁ - (1/2)gT₁² = 5
Using g = 10 & T₁ = 5/ VCosα
=> VSinα(5/ VCosα) - 5 (5/ VCosα)² = 5
=> Tanα - 25/V²Cos²α = 1
=> Tanα = 1 + 25/V²Cos²α
Let say at T₂ time Ball crosses back window
then Horizontal Distance = VCosα*T₂ = 11 m => T₂ = 11/ VCosα
& Vertical Distance = VSinαT₂ - (1/2)gT₂² = 7
Using g = 10 & T₂ = 11/ VCosα
=> VSinα(11/ VCosα) - 5 (11/ VCosα)² = 7
=> 11Tanα - 605/V²Cos²α = 7
=> Tanα = (7 + 605/V²Cos²α)/11
1 + 25/V²Cos²α = (7 + 605/V²Cos²α)/11
=> 11 + 275/V²Cos²α = 7 + 605/V²Cos²α
=> 4 = 330/V²Cos²α
=> V²Cos²α = 165/2
putting V²Cos²α = 165/2 in below
Tanα = 1 + 25/V²Cos²α
=> Tanα = 1 + 25/(165/2)
=>Tanα = 1 + 10/33
=> Tanα = 43/33
=> α = Tan⁻¹(43/33) = 52.5°
Cosα = 33/ √(33² + 43²)
=> Cos²α = 1089/2938
V²Cos²α = 165/2
=> V² (1089/2938) = 165/2
=> V² = 7345/33
=> V = 14.9 m/s