Question

A contestant on Amazing Race is using a slingshot to launch 12-kg watermelons at targets. The slingshot is pulled back 1.5 m, and the watermelon is at ground level. The launch point is 0.3 m above the ground, and the targets are 10 m away horizontally. Calculate the spring constant of the slingshot.

Which formula can be used to calculate the spring constant of the slingshot in this scenario?

a) ( k = frac{m cdot g}{x} )

b) ( k = frac{x cdot g}{m} )

c) ( k = frac{m cdot g}{x^2} )

d) ( k = frac{x^2 cdot g}{m} )

Answer 1

The spring constant of the slingshot can be calculated using the formula k = mg/x. Plugging in the values, the spring constant in this scenario is 78.4 N/m.

Step-by-step explanation:

To calculate the spring constant of the slingshot in this scenario, we can use the formula:

k = mg/x

where k is the spring constant, m is the mass of the watermelon, g is the acceleration due to gravity, and x is the distance the slingshot is pulled back.

Plugging in the values for the given scenario:

1. m = 12 kg
2. g = 9.8 m/s^2
3. x = 1.5 m

We can calculate:

k = (12 kg) * (9.8 m/s^2) / (1.5 m) = 78.4 N/m

Therefore, the spring constant of the slingshot in this scenario is 78.4 N/m.