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
The average speed is 52km
Answer:
<u>6 bulbs</u> are needed to illuminate the room.
Explanation:
Given:
Measurement of kitchen (A) = 10 ft by 10 ft = 100 sq. ft
Number of footcandles (n) = 50
Lumens emitted by 1 bulb = 834
Number of bulbs (N) = ?
We are also given,
1 foot candle = 1 lumen/sq. ft
So, 50 foot candles = 50 lumens/sq. ft
Now, for an area of 1 sq. ft 50 lumens are emitted.
So, for an area of 100 sq. ft, lumens emitted = 50 × 100 = 5000 lumens
Now, one bulb emits = 834 lumes
Therefore, number of bulbs required for emitting 5000 lumens is given as:

So, 6 bulbs are needed to illuminate the room.
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