The maximum, range of a projectile is directly proportional to the square of its velocity. A baseball pitcher throws a ball at 60 mph, with a maximum range of 242 ft. What is his maximum range if he throws the ball at 70 mph?
"The maximum, range of a projectile is directly proportional to the square of its velocity"
-----> range = k(velocity)^2 , where k is a constant
when vel=60, range = 242
242 = k(3600)
k = 242/3600 = 121/1800
r = (121/1800)v^2
when v=70
r = (121/1800)(4900) = 5929/18 = appr. 329 ft
Thanks a bunch
The range of projectile is directly proportional to
Oh, I see what's going on here. The baseball pitcher wants to increase his maximum range, so he's increasing his speed! That's quite a strategy.
Now, if the maximum range is directly proportional to the square of the velocity, let's do some calculations. We know that at 60 mph, the maximum range is 242 ft. So, if we increase the velocity to 70 mph, we just need to find out how this affects the range.
Now, let me work my calculations... *humming mathematically*
Okay, I've got it! According to my calculations (and my trusty juggling balls), the maximum range at 70 mph will be approximately... drumroll, please... 323 ft!
Congratulations to the pitcher on his increased velocity and improved range. Hope he doesn't throw the ball into someone's popcorn!
To find the maximum range of the ball thrown at 70 mph, we can use the given information about the maximum range at 60 mph.
First, let's define some variables for our problem:
v1 = initial velocity of the ball (60 mph)
r1 = maximum range of the ball at velocity v1 (242 ft)
We are given the relationship between the maximum range and the square of the velocity:
r ∝ v^2
This means that the maximum range is directly proportional to the square of the velocity. To find the constant of proportionality, we can use the given values.
Since r is directly proportional to v^2, we can express this relationship as:
r = k * v^2
Now we need to find the value of k. Using the given information:
r1 = k * v1^2
Substituting the values we have:
242 ft = k * (60 mph)^2
242 ft = k * 3600 mph^2
To solve for k, divide both sides of the equation by 3600 mph^2:
k = 242 ft / 3600 mph^2
k = 0.0672 ft/mph^2
Now we know the constant of proportionality, k. To find the maximum range at 70 mph, we can use the same formula:
r2 = k * v2^2
Substituting the values we now have:
r2 = (0.0672 ft/mph^2) * (70 mph)^2
r2 = (0.0672 ft/mph^2) * 4900 mph^2
r2 = 329.44 ft
Therefore, the maximum range of the ball thrown at 70 mph is approximately 329.44 feet.