Question

when a stone is projected with 25degree and 65degree to the horizontal its height are 1m and 4m respectively then its rang is​

Answer 1

Given info : when stone is projected with 25° and 65° to the horizontal and its heights are 1 m and 4 m respectively.

To find : the range of stone is ...

Solution : case 1 : angle of projection, α = 25° and maximum height, H = 1 m

so, u²sin²25°/2g = 1 [ using u²sin²θ/2g = Hmax]

⇒u²sin²25° = 2g ......(1)

Case 2 : angle of projection, β = 65° and maximum height, H = 4 m

so, u²sin²65°/2g = 4

⇒u²sin²65° = 8g ......(2)

From equations (1) and (2) we get,

(u²sin²25°)/(u²sin²(90°-25°)) = 2g/8g

⇒tan²25° = 1/4

so, tan25° = 1/2

sin25° = 1/√5 and cos25° = 2/√5

From equation (1),

u² (1/5) = 2g

⇒u² = 10g

Now, Range = u²sin2(25°)/g

= 10g(2sin25° cos25°)/g

= 10 × 2 × 1/√5 × 2/√5

= 20 × 2/5

= 8 m

Therefore the range of stone is 8m