Related Rates

Rachel is standing atop a 13 ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3 ft/sec. How fast is the ladder sliding down the wall when the tip of the ladder is 5 ft high?

• 3 ft/sec
• -7.2 ft/sec
• 7.2 ft/sec
• 12

Tags

CCSS.8.G.B.8

Rachel is standing atop a 13 ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3 ft/sec.  How fast is the angle between the tip of the ladder and the house changing when the ladder is 5 ft high? Hint: Use a trig function.

• 1 deg/sec
• -.5 deg/sec
• .6 deg/sec
• The angle is not changing.

Tags

CCSS.HSG.SRT.C.6

CCSS.HSG.SRT.C.8

Chris is sitting on the edge of a dock tossing rocks into the water. As each rock hits the water, small circles appear traveling outward from the point of impact. The radius of the circle is changing at a rate of 5 in/sec.  How fast is the area of the outer circle changing when the diameter is 8 in?

• 80pi in/sec
• 20pi in/sec
• 60pi in/sec
• 4opi in/sec

Tags

CCSS.HSG.GMD.A.1

CCSS.HSA.SSE.A.1

Chris is sitting on the edge of a dock tossing rocks into the water. As each rock hits the water, small circles appear traveling outward from the point of impact. The radius of the circle is changing at a rate of 5 in/sec.  How fast is the area changing when the circumference is 4 in? 

• 40 in/sec
• 20 in/sec
• 20pi in/sec
• 40pi in/sec

Tags

CCSS.HSG.GMD.A.1

Brandon is starting to clean up after a birthday party. He begins deflating each spherical balloon by puncturing a hole in each. The air leaves the balloon at a constant rate of 2 cm³/sec.  How fast is the diameter changing when the diameter is 8 cm?

• -1/(16pi) cm/sec
• -1/16 cm/sec
• -1/(4pi) cm/sec
• 1/(4pi) cm/sec

Tags

CCSS.HSG.GMD.A.3

A water tank, shaped like an inverted circular cone, has a base radius of 6 ft and a height of 9 ft. The tank is completely full and needs to be drained. The valve is opened and the water begins to decrease at a rate of 2 ft³/sec.  How fast is the height of the water changing when the water is 2 ft deep?

• -9/(8pi) ft/sec
• 9/(8pi) ft/sec
• -8/(9pi) ft/sec
• 8/(9pi) f/tsec

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GMD.A.3

CCSS.HSG.MG.A.1

A water tank, shaped like an inverted circular cone, has a base radius of 6 ft and a height of 9 ft. The tank is completely full and needs to be drained. The valve is opened and the water begins to decrease at a rate of 2 ft³/sec.  How fast is the radius changing when the water is 2 ft deep?

• 4/(3pi) ft/sec
• 3/(4pi)ft/sec
• -3/(4pi) ft/sec
• -4/(3pi) ft/sec

Tags

CCSS.HSG.GMD.A.3

CCSS.HSA.CED.A.2

Devin set up a toy rocket. For safety, he stands 6 meters from the rocket. He sets off the rocket and it heads straight up at a constant rate of 4 m/s.  How fast is the distance between the rocket and Devin changing after 2s?

• -2.5 m/s
• 2.5 m/s
• 3.2 m/s
• -3.2 m/s

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.SSE.A.1

CCSS.HSG.SRT.C.6

CCSS.HSG.SRT.C.8

CCSS.HSS.ID.C.7

Devin set up a toy rocket. For safety, he stands 6 meters from the rocket. He sets off the rocket and it heads straight up at a constant rate of 4 m/s.  How fast is the angle from Devin’s feet to the rocket changing after 2 seconds?

• 53.13 deg/sec
• -53.13 deg/sec
• .96 deg/s
• -.96 deg/sec

Tags

CCSS.HSF.TF.B.7