A soccer ball is kicked from the ground with initial speed 17 m/s. at angle(a 20 Find a) The horizontal distance that the ball travels after 4s? b) The speed of the ball at the highest point?
I guess you mean 20 degrees above horizontal.
u = horizontal velocity, does not change
= 17 cos 20
so
a) (17 cos 20)4
b) u = 17 cos 20
At the highest point, there is no vertical velocity, so the answer is u = 17 cos 20
Vi = 17 sin 20 = 5.81
t = 5.81/9.81 =.593 seconds upward
so in the air 2*.593 = 1.19 seconds in the air
so it is not in the air for five seconds
and the answer to part a is
d = u t = 17 * cos 20 * 1.19
= 19 meters
To find the horizontal distance traveled by the soccer ball, you can use the horizontal component of its initial velocity, as there is no acceleration in the horizontal direction.
a) The horizontal component of the initial velocity can be found using the formula:
Vx = V * cos(a)
where V is the initial speed of the ball and a is the angle at which it is kicked.
Given: V = 17 m/s and a = 20 degrees
Vx = 17 * cos(20)
Using a scientific calculator, find the value of cos(20) and multiply it by 17 to obtain the horizontal component of the velocity.
Once you have the value of Vx, you can use the horizontal distance formula:
Distance = Vx * time
where time (t) is 4s.
b) To find the speed of the ball at the highest point, you need to consider the vertical component of its velocity. The vertical component can be calculated using the formula:
Vy = V * sin(a)
where V is the initial speed of the ball and a is the angle at which it is kicked.
Given: V = 17 m/s and a = 20 degrees
Vy = 17 * sin(20)
Using a scientific calculator, find the value of sin(20) and multiply it by 17 to find the vertical component of the velocity.
At the highest point, the vertical velocity component becomes zero. The speed at the highest point is equal to the magnitude of the resultant velocity, which is given by:
Speed = sqrt(Vx^2 + Vy^2)
Calculate Vx and Vy using the formulas mentioned above, and substitute the values in the given formula to find the speed at the highest point.