Question

Natalie and Landon are at Color Guard practice after school. Natalie exerts a

force of 15.4 N on her baton, causing it to accelerate m/s² into the air.
Landon exerts a force of 15.1 N on his rifle, causing it to accelerate 4.2 m/s²
into the air. If both objects have 260 J of GPE, who threw theirs higher?

Answer 1

Landon threw his rifle higher than Natalie threw her baton.

Step-by-step explanation:

The gravitational potential energy (GPE) of an object is given by:

GPE = mgh

where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object.

Assuming that the baton and rifle have the same mass, we can set their GPEs equal to each other:

mgh = mgh

260 J = mgh

Now we can solve for h:

h = 260 J / (mg)

The mass cancels out, so we can use the same height formula for both objects.

For Natalie's baton:

F = ma

a = F/m

Using the given values, we get:

a = 15.4 N / m (since the mass is not given)

Now we can use the height formula:

h = 260 J / (mg)

h = 260 J / (m * 9.81 m/s²) (acceleration due to gravity)

h = 26.53 / m

h = (1/2)at²

h = (1/2)(15.4 N / m)(t²)

Setting the two expressions for height equal to each other, we get:

26.53 / m = (1/2)(15.4 N / m)(t²)

Solving for t, we get:

t = sqrt((2 * 26.53) / (15.4 N / m))

t = 1.41 s

Now we can use the time and acceleration to find the height:

h = (1/2)at²

h = (1/2)(15.4 N / m)(1.41 s)²

h = 15.33 m

For Landon's rifle, we can use the same height formula:

h = 260 J / (mg)

h = 260 J / (m * 9.81 m/s²)

h = 26.53 / m

h = (1/2)at²

h = (1/2)(15.1 N / m)(4.2 s²)

h = 35.77 m

Therefore, Landon threw his rifle higher than Natalie threw her baton.

Hope this helps!