Maria throws an apple vertically upward from
a height of 1.3 m with an initial velocity of
+2.6 m/s.
Will the apple reach a friend in a tree house
2.4 m above the ground? The acceleration
1. No, the apple will reach 1.37063 m below
the tree house
2. Yes, the apple will reach 1.37063 m above
the tree house
3. Yes, the apple will reach 0.755454 m
above the tree house
4. No, the apple will reach 0.755454 m
below the tree house
5. Yes, the apple will reach 1.48537 m above
the tree house
h = -.5 g t^2 + 2.6 t + 1.3
the max height occurs at the value of t that lies on the axis of symmetry (t = -b / 2a) __ t = -2.6 / -9.8
find t and substitute back to find the max height
DANG THE COMMENT WAS FROM 2012!!! WHOA :<
To determine whether the apple will reach the friend in the tree house, we need to use physics equations and principles.
First, let's calculate the time it takes for the apple to reach its highest point. We can use the formula:
t = (v_final - v_initial) / a
where:
- v_final is the final velocity (which will be zero at the highest point)
- v_initial is the initial velocity
- a is the acceleration (which is approximately equal to the acceleration due to gravity, g)
Given:
- v_initial = +2.6 m/s (positive because the apple is thrown upward)
- a = -9.8 m/s^2 (negative because gravity is acting downward)
Plugging the values into the equation, we have:
t = (0 - 2.6) / -9.8
= 2.6 / 9.8
≈ 0.2653 seconds
Now, let's determine the maximum height reached by the apple above the ground. We can use the formula:
d = v_initial * t + (1/2) * a * t^2
where:
- d is the displacement (which is the height reached above the initial height)
- v_initial is the initial velocity
- t is the time
- a is the acceleration (which is approximately equal to the acceleration due to gravity, g)
Given:
- v_initial = +2.6 m/s (positive because the apple is thrown upward)
- t ≈ 0.2653 seconds
- a = -9.8 m/s^2 (negative because gravity is acting downward)
- initial height = 1.3 m
Plugging the values into the equation, we have:
d = 2.6 * 0.2653 + (1/2) * (-9.8) * (0.2653)^2
≈ 0.687 m
Next, let's determine whether the apple will reach a height of 2.4 m above the ground. Given the height of the tree house is 2.4 m above the ground, we need to determine if the apple's maximum height (0.687 m) combined with the initial height (1.3 m) is greater than 2.4 m.
Therefore, the answer is 3. Yes, the apple will reach 0.755454 m above the tree house.