The use of brakes on a long, steep downgrade
1 answer:
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Answer:
The minimum average speed the opponent must move so that he is in position to hit the ball is approximately 5.79 m/s
Explanation:
The given parameters of the ball are;
The initial speed of the ball = 15 m/s
The direction in which the ball is launched = 50° above the horizontal
The location of the other tennis player when the ball is launched = 10 m from the ball
The time at which the other tennis player begins to run = 0.3 seconds after the ball is launched
The height at which the ball is hit back = 2.1 m above the height from which the ball is launched
The vertical position, 'y', at time, 't', of a projectile motion is given as follows;
y = (u·sinθ)·t - 1/2·g·t²
When y = 2.1 m, we have;
2.1 = (15·sin(50°))·t - 1/2·9.8·t²
∴ 4.9·t² - (15·sin(50°))·t + 2.1 = 0
Solving with the aid of a graphing calculator function, we get;
t = 0.199776187257 s or t = 2.14525782198 s
Therefore, the ball is at 2.1 m above the start point on the other side of the court at t ≈ 2.145 seconds
The horizontal distance, 'x', the ball travels at t ≈ 2.145 seconds is given as follows;
x = u × cos(50°) × t = 15 × cos(50°) × 2.145 ≈ 20.682 m
The horizontal distance the ball travels at t ≈ 2.145 seconds, x ≈ 20.682 m
Therefore, we have;
The time the other player has to reach the ball, t₂ =2.145 s - 0.3 s ≈ 1.845 s
The distance the other player has to run, d = 20.682 m - 10 m = 10.682 m
The minimum average speed the other player has to move with, = d/t₂
∴ = 10.682 m/(1.845 s) ≈ 5.78970189702 m/s ≈ 5.79 m/s
The minimum average speed the opponent must move so that he is in position to hit the ball, ≈ 5.79 m/s.
Answer:
(a). Their speed during that run is 10 m/s.
(b). Their velocity is 6.86 m/s
(c). The final position is at 8.91 m.
Explanation:
Given that,
A football player starts at the 40-yard line, and runs to the 25-yard line in 2 seconds.
Suppose, the distance between 40 yard line and 25 yard line is 20 yard.
(a). We need to calculate their speed during that run
Using formula of speed
Where. d = distance
t = time
Put the value into the formula
during that run
(b). We need to calculate their velocity
Using formula of speed
Put the value into the formula
Negative sign shows the direction of motion.
(c). If they kept running at that velocity for another 1.3 seconds,
We need to calculate the final position
Using formula of position
Put the value into the formula
Hence, (a). Their speed during that run is 10 m/s.
(b). Their velocity is 6.86 m/s
(c). The final position is at 8.91 m.