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Given:

Distance= 690 metres

Angle of elevation= 60°

Gravity (g)= 10 m/s²

To Find:

Initial velocity (V₀)

Solution:

For solving this question, we are going to use the horizontal range formula of projectile motion.

To find the maximum horizontal displacement, we consider the "y" component of the displacement equation to be zero,

⇒y= tanθ. x - [tex]\frac{g}{2u^{2}cos^{2}θ }[/tex]. x²

⇒0= tanθ. x - [tex]\frac{g}{2u^{2}cos^{2}θ }[/tex]. x²

⇒ Range =  u²sin2θ/g

[ u= Initial velocity, θ= angle of elevation]

[As all the quantities are in the S.I unit, no conversion is needed.]

Thus, now substituting the given values in the equation, we get,

⇒ 690= [u² × sin (2×45°)] / 10

⇒ 690= [u² × sin 90°] / 10

⇒ 690= u²/10                    ∵ [ sin 90°=1]

⇒ 690× 10= u²

⇒ √6900 = u

⇒ u= 83.066 m/sec

Hence, the Initial velocity (V₀) is 83.066 m/sec.

Answer:

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Explanation:

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Answer:

Explanation:

first ,we can find the time of flight

and we know the equation of time of flight is T=2v₀sinФ/g=2×v₀sin45/10

⇒(2×v₀×1/√2)/10⇒ T=√2v₀/10(equation 1)

we know that 690 m is the horizontal distance from the port and the horizontal component of velocity is v₀cos45=v₀×1/√2=v₀/√2

we know horizontal range(R)=v₀cosФ×T⇒ 690=(v₀/√2)×T(equation 2)

substituting equation 1 in equation 2

690=(v₀/√2)×√2v₀/10⇒ 690=v₀²/10

⇒v₀²=6900⇒ v₀=83.07m/s

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Initial velocity of shell is 10√69 m/s or about 83.066m/s

• A ship is 690 m away from port.
• Initial velocity of v₀ at an elevation of 45° with the horizontal
• Hit the ship which is stationary
• g = 10 m/s²

• Initial velocity of shell v₀

Find Vertical and horizontal component of velocity

vertical v₀sin45° = v₀/√2

Horizontal  v₀cos45° = v₀/√2

Use V = U + at  and find t to reach at top where v= 0  

0 =  v₀/√2 + gt

=> 0 =  v₀/√2 + (-10)t

=> t = v₀/10√2

Total Time of flight is double to reach top

= 2t

= 2 v₀/10√2

= √2v₀/10

Find Distance using Horizontal speed x Time and equate with 690

(v₀/√2 ) (√2v₀/10)  = 690

=>  v₀² = 6900

=>  v₀ = 10√69 m/s

 v₀ ≈ 83.066m/s

Initial velocity of shell is 10√69 m/s or about 83.066m/s