Question

A rocket moves upward, starting from rest with an acceleration of +29.4 for 3.98 s. it runs out of fuel at the end of the 3.98 s but does not stop. m/s2 how high does it rise above the ground?

Answer 1

consider the motion of rocket until it runs out of fuel

v₀ = initial velocity = 0 m/s

v = final velocity when it runs out of fuel = ?

t = time after which fuel is finished = 3.98 sec

a = acceleration = 29.4 m/s²

Y₀ = height gained when the fuel is finished = ?

using the kinematics equation

v = v₀ + a t

v = 0 + (29.4) (3.98)

v = 117.01 m/s

using the equation

v² = v²₀ + 2 a Y₀

(117.01)² = 0² + 2 (29.4) Y₀

Y₀ = 232.85 m

consider the motion of rocket after fuel is finished till it reach the maximum height.

Y₀ = initial position = 232.85 m

Y = final position at maximum height

v₀ = initial velocity just after the fuel is finished = 117.01 m/s

v = final velocity after it reach the maximum height = 0 m/s

a = acceleration due to gravity = - 9.8 m/s²

using the kinematics equation

v² = v²₀ + 2 a (Y - Y₀)

inserting the values

0² = (117.01)² + 2 (- 9.8) (Y - 232.85)

Y = 931.4 m

Answer 2

The total distance traveled by the rocket above the ground is 931.4 m.

The given parameters;

• acceleration of the rocket, a = 29.4 m/s²
• time of motion of the rock, t = 3.98 s

The distance traveled by the rocket during the 3.98 s is calculated as follows;

$h_1 = v_0t + \frac{1}{2} at^2\\\\h_1 = 0 + \frac{1}{2} (29.4)(3.98)^2\\\\h_1 = 232.85 \ m$

The final velocity of the rocket after 3.98 s is calculated as follows;

$v_i= v_0 + at\\\\v_i= 0 + (29.4 \times 3.98)\\\\v_i = 117.01 \ m/s$

"when the rocket runs out of fuel, it moves at a constant speed and the acceleration is zero. The rocket will be moving against gravity."

The distance traveled by the rocket when it runs out of fuel is calculated as follows;

$v_f^2 = v_i^2 - 2gh_2$

where;

• $v_f$ is the final velocity of the rocket at maximum height = 0

$0 = (117.01)^2 -2(9.8)h_2 \\\\2(9.8)h_2 = (117.01)^2\\\\h_2 = \frac{ (117.01)^2}{2(9.8)} \\\\h_2 = 698.54 \ m$

Total distance traveled by the rocket above the ground;

H = h₁ + h₂

H = 232.85 m + 698.54 m

H = 931.4 m

Thus, the total distance traveled by the rocket above the ground is 931.4 m.

Learn more here:https://brainly.com/question/10180477