The goalkeeper at his goal cannot kick a soccer ball into the opponent’s goal without the ball touching the ground
Explanation:
Consider the vertical motion of ball,
We have equation of motion v = u + at
Initial velocity, u = u sin θ
Final velocity, v = 0 m/s
Acceleration = -g
Substituting
v = u + at
0 = u sin θ - g t

This is the time of flight.
Consider the horizontal motion of ball,
Initial velocity, u = u cos θ
Acceleration, a =0 m/s²
Time,
Substituting
s = ut + 0.5 at²

This is the range.
In this problem
u = 30 m/s
g = 9.81 m/s²
θ = 45° - For maximum range
Substituting

Maximum horizontal distance traveled by ball without touching ground is 45.87 m, which is less than 95 m.
So the goalkeeper at his goal cannot kick a soccer ball into the opponent’s goal without the ball touching the ground
Answer:

Explanation:
<u>Motion with Constant Acceleration</u>
A body moves with constant acceleration when the speed changes uniformly in time. The equation used to find the final speed vf is

Where vo is the initial speed, a is the acceleration, and t is the time.
The cyclist has an initial speed of vo=10 miles/hour and ends up at vf=20 miles/hour in t=5 seconds.
Both speeds are given in miles/hour and we must convert it to m/s:
1 mile/hour = 0.44704 m/s
10 mile/hour = 4.47 m/s
20 mile/hour = 8.94 m/s
The acceleration is calculated by solving for a:



Wavelength = c/f.
Wavelength =0.5km