3. A point Q is d metres from a line L. The curve C has the property that the distance from any point on C to Q is the same as the distance from that point to the line L. (The distance will depend on the point.) Here is a picture to show what that means. 13 L An object is travelling along the curve and casts a shadow on L. Let e(t) be the distance from Q to the object, 0(t) the angle that the line connecting Q to the object makes with a vertical line, and x(t) the distance from the shadow to the vertical line, all at time t. cbject shadow 1 At a certain point in time to l(t) = 12m, 0(t) = radians, and the shadow of the object on L is travelling at 5 m/s to the right. QUESTION: How fast are l and 6 changing at time t,? To answer this, (a) Write down a formula for (t) involving e(t) and 8(t). (6) Write down an equation involving ((t) and e(t) which expresses the condition "The distance from the object to Q is the same as the distance from the object to L" (c) Use the formulas in (a) and (b) to answer the question above (don't forget the units). 3. A point Q is d metres from a line L. The curve C has the property that the distance from any point on C to Q is the same as the distance from that point to the line L. (The distance will depend on the point.) Here is a picture to show what that means. 13 L An object is travelling along the curve and casts a shadow on L. Let e(t) be the distance from Q to the object, 0(t) the angle that the line connecting Q to the object makes with a vertical line, and x(t) the distance from the shadow to the vertical line, all at time t. cbject shadow 1 At a certain point in time to l(t) = 12m, 0(t) = radians, and the shadow of the object on L is travelling at 5 m/s to the right. QUESTION: How fast are l and 6 changing at time t,? To answer this, (a) Write down a formula for (t) involving e(t) and 8(t). (6) Write down an equation involving ((t) and e(t) which expresses the condition "The distance from the object to Q is the same as the distance from the object to L" (c) Use the formulas in (a) and (b) to answer the question above (don't forget the units). 3. A point Q is d metres from a line L. The curve C has the property that the distance from any point on C to Q is the same as the distance from that point to the line L. (The distance will depend on the point.) Here is a picture to show what that means. 13 L An object is travelling along the curve and casts a shadow on L. Let e(t) be the distance from Q to the object, 0(t) the angle that the line connecting Q to the object makes with a vertical line, and x(t) the distance from the shadow to the vertical line, all at time t. cbject shadow 1 At a certain point in time to l(t) = 12m, 0(t) = radians, and the shadow of the object on L is travelling at 5 m/s to the right. QUESTION: How fast are l and 6 changing at time t,? To answer this, (a) Write down a formula for (t) involving e(t) and 8(t). (6) Write down an equation involving ((t) and e(t) which expresses the condition "The distance from the object to Q is the same as the distance from the object to L" (c) Use the formulas in (a) and (b) to answer the question above (don't forget the units). 3. A point Q is d metres from a line L. The curve C has the property that the distance from any point on C to Q is the same as the distance from that point to the line L. (The distance will depend on the point.) Here is a picture to show what that means. 13 L An object is travelling along the curve and casts a shadow on L. Let e(t) be the distance from Q to the object, 0(t) the angle that the line connecting Q to the object makes with a vertical line, and x(t) the distance from the shadow to the vertical line, all at time t. cbject shadow 1 At a certain point in time to l(t) = 12m, 0(t) = radians, and the shadow of the object on L is travelling at 5 m/s to the right. QUESTION: How fast are l and 6 changing at time t,? To answer this, (a) Write down a formula for (t) involving e(t) and 8(t). (6) Write down an equation involving ((t) and e(t) which expresses the condition "The distance from the object to Q is the same as the distance from the object to L" (c) Use the formulas in (a) and (b) to answer the question above (don't forget the units)