Please explain it step by tep. Thank!!!!....
Goldberg's sleigh currently runs at 203mph, but he needs it to reach 400mph with all the packages he has to deliver. If Goldberg is delivering presents at an altitude of 5,813.6ft, with the same drag and weight of a 2019 Challenger SRT® Hellcat Redeye, how much HP would he need to reach 400 mph? Pro Tips • 100% driveline efficiency • P (air density) at 5813.6 ft = .0019 slug/ft^3 • A (Area of Challenger front end) = 26.72 ft2 • C(d) (Coefficient of drag) = .398 • Goldberg's sleigh required speed, 400 MPH = 587 ft/sec • F(drag) = 1/2 px v^2 x C(d)A • P = F(drag) x V • Convert to Horsepower = P( 1HP/550 ft lbf/sec)
To calculate the horsepower (HP) needed for Goldberg's sleigh to reach 400 mph, we will use the formula provided. Let's break it down step by step:
Step 1: Calculate the drag force (F(drag))
Use the formula F(drag) = (1/2) x P x v^2 x C(d) x A, where:
- P is the air density: P = 0.0019 slug/ft^3
- v is the velocity (sleigh required speed): v = 587 ft/sec
- C(d) is the coefficient of drag: C(d) = 0.398
- A is the area of the Challenger front end: A = 26.72 ft^2
Plug in the values:
F(drag) = (1/2) x 0.0019 x 587^2 x 0.398 x 26.72
Simplify the equation:
F(drag) = 0.0019 x 342,769 x 0.398 x 26.72
Step 2: Calculate the power required (P)
Use the formula P = F(drag) x v
Plug in the values:
P = (0.0019 x 342,769 x 0.398 x 26.72) x 587
Simplify the equation:
P = 4,044.8406 x 587
Step 3: Convert power to horsepower
Use the conversion factor 1 HP = 550 ft lbf/sec
P (in horsepower) = P / (550 ft lbf/sec)
Plug in the value:
P (in horsepower) = (4,044.8406 x 587) / 550
Simplify the equation:
P (in horsepower) ≈ 4317.9258 / 550
P (in horsepower) ≈ 7.8507 HP
Therefore, Goldberg's sleigh would need approximately 7.85 horsepower to reach 400 mph with all the given parameters.