The Elevator Scene In Captain America – Winter Soldier, Is Considered One Of The Marvel Series Most Iconic. Cap Singlehandedly Incapacitates 10 Agents Before Jumping Out Of The Glass Elevator From 20 Floors Up. Cap Leaps With An Initial Speed Vo – 6.75 M/S At An Angle Of 20 Above The Horizontal (See Figure). If He Falls A Vertical Distance Of 90.0 M, With
The Correct Answer and Explanation is :
To solve this problem, we analyze Captain America’s motion using kinematic equations. This is a projectile motion problem where Cap jumps from a height of 90.0 m with an initial velocity of 6.75 m/s at an angle of 20° above the horizontal.
Step 1: Break Down Initial Velocity
We decompose the velocity into horizontal and vertical components:
- Horizontal velocity:
[
V_{0x} = V_0 \cos(20^\circ) = 6.75 \times \cos(20^\circ)
]
[
V_{0x} \approx 6.75 \times 0.9397 = 6.34 \text{ m/s}
] - Vertical velocity:
[
V_{0y} = V_0 \sin(20^\circ) = 6.75 \times \sin(20^\circ)
]
[
V_{0y} \approx 6.75 \times 0.3420 = 2.31 \text{ m/s}
]
Step 2: Time of Flight
Using the vertical motion equation:
[
y = V_{0y} t + \frac{1}{2} g t^2
]
Since he falls 90.0 m, we set ( y = -90.0 ) m, ( V_{0y} = 2.31 ) m/s, and acceleration due to gravity ( g = -9.81 ) m/s²:
[
-90.0 = 2.31 t – \frac{1}{2} (9.81) t^2
]
[
-90.0 = 2.31t – 4.905t^2
]
Rearrange:
[
4.905t^2 – 2.31t – 90.0 = 0
]
Solving using the quadratic formula:
[
t = \frac{-(-2.31) \pm \sqrt{(-2.31)^2 – 4(4.905)(-90.0)}}{2(4.905)}
]
[
t = \frac{2.31 \pm \sqrt{5.3361 + 1761.8}}{9.81}
]
[
t = \frac{2.31 \pm \sqrt{1767.14}}{9.81}
]
[
t = \frac{2.31 \pm 42.04}{9.81}
]
[
t = \frac{2.31 + 42.04}{9.81} = \frac{44.35}{9.81} \approx 4.52 \text{ s}
]
(Since time cannot be negative, we take the positive value.)
Step 3: Horizontal Distance
[
x = V_{0x} t
]
[
x = (6.34)(4.52) = 28.66 \text{ m}
]
Final Answer
Captain America lands 28.7 meters away from the elevator base after falling.