A boy pulls a 47.5 kg crate with a rope. The rope makes an angle of 28.0° to the horizontal.
1 answer:
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Answer:
a) h / h₀ = 1,682
, b) h / h₀ = 1.11
, c) h / h₀ = 2.07
Explanation:
For this exercise let's look for the growth equation, as they indicate that it is exponential
h = h₀
The initial height is 9 ”, so the constant
h₀ = 9”
Let's use the given values
h = 15.1655”
t = 5 days
h / h₀ =
α = 1 / t ln h / h₀
α = 1/5 ln (15.1655 / 9)
α = 0.104
h = 9 e^{0.104 t}
a) the growth factor is the relationship between the initial value and the current value
h / h₀ =
h / h₀ = 1,682
b) for t = 1 day
h / h₀ =
h / h₀ = 1.11
c) for t = 7 days
h / h₀ = e^{0.104 7}
h / h₀ = 2.07
Answer:
A. xmax = 131.49 m
B. t = 8.74 s
C. ymax = 220.33 m
Explanation:
A. In order to find the horizontal distance which cannon travels you first calculate the flight time. The flight time can be calculated by using the following formula:
(1)
yo: height from the projectile is fired = 200m
vo: initial velocity of the projectile = 25m/s
g: gravitational acceleration = 9.8 m/s^2
θ: angle between the direction of the initial motion of the ball and the horizontal = 53°
t: time
You need the value of t when the projectile hits the ground. Then, in th equation (1) you make y = 0m.
When you replace the values of all parameters in the equation (1), you obtain the following quadratic formula:
(2)
You use the quadratic formula to obtain the value of t:
You use the positive value because it has physical meaning.
Now, you can calculate the horizontal range of the projectile by using the following formula:
The cannon ball travels a horizontal distance of 131.49 m
B. The cannon ball reaches the canon for t = 8.74s
C. The maximum height is obtained by using the following formula:
(3)
By replacing in the equation (3) the values of all parameters you obtain:
The maximum height reached by the cannon ball is 220.33m