Answer:
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!