Last year the varsity WDV boys basketball team made it to the semi-finals and only needed to win two more games to go play in the Finals. The team's travel plan was to leave Los Angeles and travel 138 miles north to
the town of Santa Maria to play the first team. After winning that game, they would travel from Santa Maria
southeast to Tehachapi to play the second team. Finally, the team would travel 97 miles to return home for
their final game.
The team bus can travel only 300 miles on one tank of gas. Assuming that all of the roads connecting the
three towns are straight and that the two roads that connect in Los Angeles form a 28° angle, will one tank of
gas be enough for the trip? Justify your solution.

a) Max height it will reach is 327.55 ft above the ground

b) It will reach max height after 5.1 seconds

c) It will be 300 feet off the ground at 12 seconds

d) It will be 305 ft above the ground

e) The rocket will be 247.55 ft above the ground after seven seconds

Step-by-step explanation:

a) Using the equations of kinematics:

v² = v_i² + 2 g Δy

where

Therefore,

0² = 50² + 2(- 9.8) Δy        

(the negative sign shows that the positive direction is upwards. Gravity acts downwards)

Δy = -(50)² / 2(-9.8)

Δy = 127.55 ft

Thus, the maximum height that the rocket reaches will be

200 ft  + 127.55 ft

= 327.55 ft above the ground

b) Using the equations of kinematics:

Δy = [(v + v_i) / 2 ] × t

t = Δy / [(v + v_i) / 2 ]

t = 127.55 / [(0 + 50) / 2]

t = 5.1 seconds

Therefore, the rocket will reach its maximum height after 5.1 seconds.

c) Using the equations of kinematics:

t₃₀₀ = Δy / [(v + v_i) / 2 ]

t₃₀₀ = 300 / [(0 + 50) / 2]

t₃₀₀ = 12 seconds

Therefore, the rocket will reach 300 feet after 12 seconds

d) Using the equations of kinematics:

Δy = [(v + v_i) / 2 ] × t

Δy = [(0 + 50) / 2] × 4.2

Δy = 105 ft

Therefore, the rocket will be

105 ft + 200 ft

= 305 ft above the ground after 4.2 seconds

e) Using the equations of kinematics:

Δy = [(v + v_i) / 2 ] × t

Δy = [(0 + 50) / 2] × 7

Δy = 175 ft

Therefore,

175 - 127.55 = 47.55 ft

Thus, the rocket will be

47.55 ft + 200 ft

= 247.55 ft above the ground after seven seconds