How Do You Calculate Football's Velocity and Time to Reach Maximum Height?

[mohammed1992]

Question :
A boy kicked a football with an initial velocity component of 15.0m/s and a horizontal velocity component of 22.0m/s.
a)what is the velocity of the football(magnitude and direction)
b)how much time is needed to reach the maximum height?

(this is not my homework,it is a question which was not been discussed in class so I am not able to answer it.)

 

[tiny-tim]

Welcome to PF!

Hi mohammed1992! Welcome to PF!

(you mean "initial vertical component" )

I assume you can do (a).

For (b), you should have used the usual https://www.physicsforums.com/library.php?do=view_item&itemid=204" equations …

show us what you've tried, and where you're stuck, and then we'll know how to help!

(same for your other thread )

 

[nlightner]

a) The velocity of the football can be calculated using the Pythagorean theorem to find the magnitude and the inverse tangent function to find the direction. The magnitude of the velocity can be calculated as √(15.0^2 + 22.0^2) = 26.9 m/s. To find the direction, we can use the inverse tangent function, tan^-1(22.0/15.0) = 55.3°. Therefore, the velocity of the football is 26.9 m/s at an angle of 55.3° above the horizontal.

b) To find the time needed to reach the maximum height, we can use the equation for vertical displacement, h = v0t - 0.5gt^2, where h is the maximum height, v0 is the initial vertical velocity component, and g is the acceleration due to gravity. Since the initial vertical velocity component is 15.0 m/s and the acceleration due to gravity is 9.8 m/s^2, we can set the equation equal to 0 and solve for t. 0 = 15.0t - 4.9t^2. Solving for t, we get t = 3.06 seconds. Therefore, it will take 3.06 seconds for the football to reach its maximum height.