When an airplane leaves the runway, its angle of climb is 24° and its speed is 345 feet per second. How long will it take the plane to climb to an altitude of 10,000 feet? 16,000 feet? (Round your answers to one decimal place.)
10,000 ft = ? in s
16,000 ft = ? in s
Vo = 345Ft/s[24o].
Xo = 345*Cos24 = 315 Ft/s.
Yo = 345*sin24 = 140 Ft/s.
Y^2 = Yo^2 + 2g*h.
0 = 140^2 - 64*h. h = 306.25 Ft., max.
Based on the information given, the plane can reach a maximum ht. of only 306 Ft.
Correction: The plane is not a free-fall object.
a. d = Yo*t.
10,000 = 140*t, t = ?.
b. 16,000 = 140*t, t = ?.
To find the time it takes for the airplane to climb to a certain altitude, we can use trigonometry. We will first find the vertical component of the airplane's velocity using the angle of climb.
Given:
Angle of climb (θ) = 24°
Speed (s) = 345 feet per second
Altitude 1 (h1) = 10,000 feet
Altitude 2 (h2) = 16,000 feet
Step 1: Find the vertical component of the velocity.
The vertical component of the velocity (v_vertical) can be found by multiplying the speed (s) by the sine of the angle of climb (θ).
v_vertical = s * sin(θ)
v_vertical = 345 * sin(24°)
Step 2: Calculate the time it takes to reach each altitude.
The time it takes (t) is equal to the altitude divided by the vertical component of the velocity.
t = h / v_vertical
Now, let's calculate the time it takes to reach 10,000 feet and 16,000 feet.
For 10,000 feet:
t1 = 10,000 / v_vertical
For 16,000 feet:
t2 = 16,000 / v_vertical
To calculate these values, we need to find the vertical component of the velocity (v_vertical) by multiplying the speed (s) by the sine of the angle of climb (θ), which we already calculated.
Now let's substitute the values and calculate the results:
v_vertical = 345 * sin(24°)
v_vertical ≈ 345 * 0.404
v_vertical ≈ 139.38 feet per second
Now, let's calculate the times:
For 10,000 feet:
t1 = 10,000 / 139.38
t1 ≈ 71.7 seconds (rounded to one decimal place)
For 16,000 feet:
t2 = 16,000 / 139.38
t2 ≈ 114.9 seconds (rounded to one decimal place)
Therefore, it will take approximately 71.7 seconds to climb to an altitude of 10,000 feet and approximately 114.9 seconds to climb to an altitude of 16,000 feet.