A follows a path gives by y = x - 1/70 x^3 (distances in miles).If the horizonta

Question

A follows a path gives by y = x - 1/70 x^3 (distances in miles).If the horizontal velocity is given by v_2 = x. find the magnitude and direction of the velocity when the the ground (assume level ) if is in minutes. Find the magnitude of the velocity of the point. The magnitude is appropriate 18.7 miles per minute. (Type an integer or a decimal. Round the final answer to one decimal place as needed. Round all intermediate values to two decimal places as needed.) Find the direction of the velocity of the point. Enter an angle theta such that 0 degree lessthanorequalto theta

Explanation / Answer

The curve y = x - x³/70 = x(1 - x²/70) is the trajectory of the rocket.
It touch the ground (y = 0) at 2 position corresponding to x = 0 (point of depart of the rocket) and x = 70, supposing x 0 (hit point)
During its flight, the velocity vector of the rocket is always tangential to the trajectory. Supposed that the velocity makes an angle with the x-axis, tan is the slope of the tangent line to the trajectory and is given by
tan = dy/dx
. . . .= 1 - 3x²/70
At the hit point, x = 70
tan = 1 - 3(70)/70 = -2,
Direction of v
v makes with the x-axis an angle equal to
= tan^-1 (-2) = -63.43°
Magnitude of v is equal to
v = v_x/cos
At hit point, v_x = x = 70 and
v = 70/cos(-63.43°)
. = 18.70506 km/minute

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.