A spring-loaded dart gun is used to shoot a dart straight up into the air. When fully compressed, the dart reaches a maximum height of h₁ above its release point. The same dart is shot up a second time from the same gun, but this time the spring is compressed at 1/2.14 as compared to the first shot. How high, h₂, does the dart go the second time in terms of the maximum height h₁? Fill in the missing factor below. (Neglect friction and assume the spring is ideal.) [Hint: Use the first situation to find an expression for the spring constant. Use that expression to solve for the height in the second situation.] h₁ h₂

College Physics
11th Edition
ISBN:9781305952300
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Chapter1: Units, Trigonometry. And Vectors
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A spring-loaded dart gun is used to shoot a dart straight up into the air. When fully compressed, the dart reaches a maximum height of \( h_1 \) above its release point. The same dart is shot up a second time from the same gun, but this time the spring is compressed at \( 1/2.14 \) as compared to the first shot.

How high, \( h_2 \), does the dart go the second time in terms of the maximum height \( h_1 \)? Fill in the missing factor below. (Neglect friction and assume the spring is ideal.)

[Hint: Use the first situation to find an expression for the spring constant. Use that expression to solve for the height in the second situation.]

\[ h_2 = \, \_\_\_\_\_ \, h_1 \]
Transcribed Image Text:A spring-loaded dart gun is used to shoot a dart straight up into the air. When fully compressed, the dart reaches a maximum height of \( h_1 \) above its release point. The same dart is shot up a second time from the same gun, but this time the spring is compressed at \( 1/2.14 \) as compared to the first shot. How high, \( h_2 \), does the dart go the second time in terms of the maximum height \( h_1 \)? Fill in the missing factor below. (Neglect friction and assume the spring is ideal.) [Hint: Use the first situation to find an expression for the spring constant. Use that expression to solve for the height in the second situation.] \[ h_2 = \, \_\_\_\_\_ \, h_1 \]
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