Derivatives  chain rule
An airplane, flying horizontally at an altitude of 1 mile, passes directly over an observer. If the constant speed of the airplane is 400 miles per hour, how fast is its distance from the observer increasing 45 seconds later? Hint: note that in 45 seconds (3/4 * 1/60 = 1/80), the airplane goes 5 miles.
 👍
 👎
 👁
 ℹ️
 🚩
1 answer

the distance z is found using
z^2 = 1^2 + x^2
at x=5, z^2 = 26
z dz/dt = x dx/dt
so at the moment in question
√26 dz/dt = 5*400
note that z will be in mi/hr 👍
 👎
 ℹ️
 🚩
answered by Steve
Answer this Question
Related Questions

Physics
A cargo plane is flying horizontally at an altitude of 10000m with a velocity of 800km/h when a cargo pallet falls out the back ramp. (i) How long does it take to fall to the ground? (ii) How far horizontally is the pallet from where it fell off when it
 asked by Olumide Adesiyan
 3,771 views

Calculus
An airplane flies at an altitude of y = 5 miles toward a point directly over an observer (see figure). The speed of the plane is 500 miles per hour. Find the rates at which the angle of elevation 𝜃 is changing when the angle is 𝜃 = 45°, 𝜃 = 60°,
 asked by Roger
 3,712 views

Physics
"An airplane is climbing at an angle of 15 degrees to the horizontal with the sun directly overhead. The shadow of the airplane is observed to be moving across the ground at 200 km/h. How long does it take for the plane to increase its altitude by 1000 m"?
 asked by Stuck
 2,978 views

Calculus
An airplane is flying in still air with an airspeed of 325 miles per hour. If it is climbing at an angle of 20°, find the rate at which it is gaining altitude.
 asked by Mary
 9,411 views

physics
You're in an airplane that flies horizontally with speed 860 km/h (240 m/s ) when an engine falls off. Neglecting air resistance, assume it takes 26 s for the engine to hit the ground. Hight of airplane is: H = 3.3 km horizontal distance that the aircraft
 asked by aaron
 5,479 views

physics
Spymaster Paul, flying a constant 215 km/h horizontally in a low flying helicopter, wants to drop secret documents into his contact's open car which is traveling 155 km/h on a level highway 78.0 m below. At what angle ( to the horizontal) should the car be
 asked by Danielle
 1,235 views

physics
An airplane is flying horizontally at a velocity of 50.0 m/s at an altitude of 125 m. It drops a package to observers on the ground below. Approximately how far will the package travel in the horizontal direction from the point that it was dropped
 asked by Nana
 2,210 views

modern physics
a hunter on the ground fires a bullet in the northeast direction which strikes a deer 0.25 metre away from him, the bullet travel with a speed of 1800m/hr.at the instant an airplane is directly over the hunter at an altitude of one metre and is traveling
 asked by martin
 1,221 views

math
An airplane is flying at an altitude of 4000 feet and descends at rate of 200 feet per minute. Determine whether the altitude is proportional to the number of minutes.
 asked by gage
 1,792 views

science**
which of the following situations would be mist similar to an electrical current passing through a metal wire in a closed circuit? A. hot water moving through a pipe B. an automobile traveling through a tunnel C. an airplane flying through clouds D. a
 asked by Anonymous
 1,575 views

proportional relationship
An airplane is flying at an altitude of 4000 feet and descends at a rate of 200 feet per min. Determine whether the altitude is proportional to the # of min.
 asked by Regan
 1,890 views

physics
An airplane is flying with a velocity of 95.0 at an angle of 26.0 above the horizontal. When the plane is a distance 113 directly above a dog that is standing on level ground, a suitcase drops out of the luggage compartment. How far from the dog will the
 asked by Supriya
 3,220 views

calc
A plane flies horizontally at an altitude of 5 km and passes directly over a tracking telescope on the ground. When the angle of elevation is π/3, this angle is decreasing at a rate of π/3 rad/min. How fast is the plane traveling at that time?
 asked by kirsten
 2,242 views

Math (Integrals)
Find the indefinite integral in two ways. ∫(2x1)^2 dx The first way I used was using the power rule and chain rule with substitution. Let u = 2x  1 du = 2 dx (1/2)∫ u^2 du (Applying power rule) (1/2) * (u^3/3) + C =(2x1)^3/6 + C What would be
 asked by Ray
 401 views

Physics
A cup of coffee is on a table in an airplane flying at a constant altitude and a constant velocity. The coefficient of static friction between the cup and the table is 0.420 . Suddenly, the plane accelerates forward, its altitude remaining constant. What
 asked by Kristyn
 3,531 views

trigonometry
An airplane is flying at an elevation of 5150 ft, directly above a straight highway. Two motorists are driving cars on the highway on opposite sides of the plane, and the angle of depression to one car is 35° and to the other is 55°. How far apart are
 asked by heather
 4,773 views

math cal
A plane flying horizontally at an altitude of 3 mi and a speed of 480 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 6 mi away from the station. (Round to the nearest
 asked by anna
 7,906 views

Calc
An airplane is flying at a speed of 350 mi/h at an altitude of one mile and passes directly over a radar station at time t=0. a) Express the horizontal distance d (in miles) that the plane has flown as a function of t. I really don't know... would it be
 asked by Justin
 2,095 views

Calc
How do I do this related rates problem? A plane flying horizontally at an altitude of 1 mi and a speed of 510 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 6 mi away
 asked by Derick
 1,029 views

Trigonometry
A passenger in an airplane flying at an altitude of 10 kilometers sees two towns directly to the left of the plane. The angles of depression to the towns are 28° and 55°. How far apart are the towns?
 asked by AwesomeGuy
 4,126 views
Still need help?
You can ask a new question or browse existing questions.