A baseball player throws a baseball directly upward into the air. The height of the ball is given by the equation y=−4.9x^2+89.5x+1.75 where y is the height in meters and x is the time in seconds. Is this equation a reasonable model for the ball's trajectory? Explain(1 point)
a) No, the initial height is 1.75 meters, which is much taller than any person.
b) No, the equation does not match the model for projectile motion.
c) No, the initial velocity would be 89.5 meters per second. This is approximately 200 miles per hour, which is faster than any human can throw a baseball.
d) Yes, the equation matches the model for projectile motion, so it is a reasonable model for the ball's trajectory.
The equation y=−16x2+275 models the height of a projectile where y is the height in meters and x is the time in seconds. Which of the following situations is the real-world scenario that is best modeled by the given equation?(1 point)
a) A ball being dropped from shoulder height.
b) A child tossing a ball into the air.
c) A stone being dropped off of the edge of a cliff.
d) A tennis ball being launched into the air by a tennis racket.
your turn to provide some input.
ahhh you should know by now im terrible at math. if i get hint i could be could good but its word problems that kills me
please someone help me with this... this makes no sense and i have to get a good grade.
#1 D Your previous problem used the same equation
#2 C The 275 is the initial height
Best duo of 2021 lol
For the first question, to determine if the given equation is a reasonable model for the ball's trajectory, we need to consider the factors mentioned in the options.
a) The initial height being 1.75 meters does not make this equation unreasonable as it is still a possible starting point for a baseball player throwing a ball.
b) The statement says that "the equation does not match the model for projectile motion." However, it does not elaborate on why the equation does not match, so it is not a valid reason to reject the model.
c) The option says that "the initial velocity would be 89.5 meters per second." While this seems fast for a human, the equation does not specify the velocity explicitly. The coefficient of the x term does represent the initial velocity, but it does not necessarily mean it is physically impossible for a human to throw a ball at that speed. Therefore, this reason is not valid either.
d) This option claims that the equation matches the model for projectile motion, which is exactly what we are testing to determine. Given that all other options are either invalid or inconclusive, we can conclude that this option is the most reasonable. Therefore, the correct answer is d) Yes, the equation matches the model for projectile motion, so it is a reasonable model for the ball's trajectory.
For the second question:
a) A ball being dropped from shoulder height does not fit the given equation because the equation assumes an initial velocity for the projectile. In this scenario, the ball is not given an initial velocity but rather starts at rest.
b) A child tossing a ball into the air can describe the scenario best modeled by the given equation. The equation accounts for both the initial velocity and the effect of gravity on the ball's height over time.
c) A stone being dropped off the edge of a cliff also does not fit the given equation. In this scenario, the stone starts at rest and is only affected by gravity, not an initial velocity.
d) A tennis ball being launched into the air by a tennis racket can also be a valid scenario for the given equation if the launch is considered as the initial velocity.
Considering the given equation, the best real-world scenario modeled by the equation is b) A child tossing a ball into the air.