A model rocket is launched from rest with an upward acceleration of 5.50 m/s^2 and, due to a strong wind, a horizontal acceleration of 1.50m/s^2 . How far is the rocket from the launch pad 7.20 later when the rocket engine runs out of fuel?

t = 7.2 Minutess?

t = 7.2min * 60s/min = 432 s.

X = Hor = 1.50 m/s^2.
Y = Ver. = 5.5 m/s^2.
R = Resultant acceleration.

R^2 = X^2 + Y^2. 1.5^2 + 5.5^2 = 32.5
R = 5.7 m/s^2.

d = Vo*t + 0.5a*t^2
d = 0 + 2.85*(432)^2 = 531,878 m.

To find the distance the rocket traveled horizontally, we can use the formula:

distance = initial velocity * time + (1/2) * acceleration * time^2

The initial velocity of the rocket in the horizontal direction is 0 m/s, since it starts from rest. The horizontal acceleration is 1.50 m/s^2, and the time is 7.20 seconds.

So, we can substitute these values into the formula:

distance = 0 * 7.20 + (1/2) * 1.50 * (7.20)^2

Calculating this equation step by step, we get:

distance = 0 + 0.5 * 1.50 * 51.84

distance = 0 + 0.5 * 77.76

distance = 0 + 38.88

Therefore, the rocket is approximately 38.88 meters away from the launch pad after 7.20 seconds when the rocket engine runs out of fuel.

To find the distance the rocket is from the launch pad, we need to calculate the horizontal distance traveled by the rocket in 7.20 seconds.

First, let's calculate the horizontal component of the velocity of the rocket. Since there is no initial horizontal velocity, the horizontal component remains constant throughout the motion. We can use the equation:

v = a * t

where:
- v is the final velocity, which in this case is the horizontal velocity
- a is the horizontal acceleration, given as 1.50 m/s^2
- t is the time, given as 7.20 seconds

Substituting the values into the equation:

v = 1.50 m/s^2 * 7.20 s
v = 10.80 m/s

Now, we can determine the horizontal displacement using the formula:

d = v * t

where:
- d is the horizontal displacement or distance traveled
- v is the horizontal velocity, calculated as 10.80 m/s
- t is the time, given as 7.20 seconds

Substituting the values into the equation:

d = 10.80 m/s * 7.20 s
d = 77.76 m

Therefore, the rocket is approximately 77.76 meters away from the launch pad after 7.20 seconds when the rocket engine runs out of fuel.