A golfer strikes a golf ball as shown. The ball leaves the club with an initial velocity of 74 m s⁻¹ at an angle of 31° to the horizontal. Which row in the table shows the horizontal and vertical components of the initial velocity of the golf ball? | Horizontal component of the initial velocity of the golf ball (m s⁻¹) | Vertical component of the initial velocity of the golf ball (m s⁻¹) | | A 38 | 44 | | B 38 | 44 | | C 44 | 63 | | D 63 | 38 | | E 63 | 44 |

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A golfer strikes a golf ball as shown - Scottish Highers Physics - Question 5 - 2023

Question 5

A golfer strikes a golf ball as shown. The ball leaves the club with an initial velocity of 74 m s⁻¹ at an angle of 31° to the horizontal. Which row in the table s... show full transcript

Worked Solution & Example Answer:A golfer strikes a golf ball as shown - Scottish Highers Physics - Question 5 - 2023

Step 1

Calculate the Horizontal Component of the Initial Velocity

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Answer

To find the horizontal component of the velocity (vₓ), we use the formula:

$vₓ = v imes ext{cos}( heta)$

Where:

$v = 74 \, \text{m s}^{-1}$
$heta = 31°$

Thus, substituting the values gives:

$vₓ = 74 imes \text{cos}(31) \approx 74 imes 0.8572 \approx 63.4 \, \text{m s}^{-1}$

This rounds to 63 m s⁻¹.

Step 2

Calculate the Vertical Component of the Initial Velocity

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Answer

To find the vertical component of the velocity (vᶧ), we use the formula:

$vᶧ = v imes ext{sin}( heta)$

Substituting the same values:

$vᶧ = 74 imes \text{sin}(31) \approx 74 imes 0.5150 \approx 38.2 \, \text{m s}^{-1}$

This rounds to 38 m s⁻¹.

Step 3

Final Answer

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Answer

Based on the calculations:

Horizontal component: 63 m s⁻¹
Vertical component: 38 m s⁻¹

Thus, the correct answer is D.

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