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A hurler strikes a sliotar with an initial velocity of 41 m s⁻¹ at an angle of 30° to the horizontal - Leaving Cert Physics - Question a - 2015

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A hurler strikes a sliotar with an initial velocity of 41 m s⁻¹ at an angle of 30° to the horizontal. How far does the ball travel horizontally in three seconds?

Worked Solution & Example Answer:A hurler strikes a sliotar with an initial velocity of 41 m s⁻¹ at an angle of 30° to the horizontal - Leaving Cert Physics - Question a - 2015

Step 1

Calculate the horizontal component of the velocity (v_h)

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Answer

To find the horizontal component of the initial velocity, we use the formula:

vh=viimesextcos(heta)v_h = v_i imes ext{cos}( heta)

where:

  • vi=41 extms−1v_i = 41 \, ext{m s}^{-1} (initial velocity)
  • θ=30exto\theta = 30^ ext{o} (angle)

Substituting in the values:

vh=41 extms−1×extcos(30exto)=41×32≈35.51 extms−1v_h = 41 \, ext{m s}^{-1} \times ext{cos}(30^ ext{o}) = 41 \times \frac{\sqrt{3}}{2} \approx 35.51 \, ext{m s}^{-1}

Step 2

Calculate the horizontal distance traveled in three seconds (s)

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Answer

Using the horizontal distance formula:

s=vh×ts = v_h \times t

where:

  • vh≈35.51 extms−1v_h \approx 35.51 \, ext{m s}^{-1} (horizontal velocity)
  • t=3 extst = 3 \, ext{s} (time)

Substituting in the values:

s=35.51 extms−1×3=106.53 extms = 35.51 \, ext{m s}^{-1} \times 3 = 106.53 \, ext{m}

Thus, the ball travels approximately 106.53 meters horizontally in three seconds.

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