143747 A girl standing on road holds her umbrella at \(45^{\circ}\) with the vertical to keep the rain away. If she starts running without umbrella with a speed of \(15 \sqrt{2} \mathrm{kmh}^{-1}\), the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is
143749 When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed \(v\), he sees that rain drops are coming at an angle \(60^{\circ}\) from the horizontal. On further increasing the speed of the car to \((1+\beta) \mathrm{v}\), this angle changes to \(45^{\circ}\). The value of \(\beta\) is close to
143750 Ship \(A\) is sailing towards north-east with velocity \(v=30 \hat{i}+50 \hat{j} \quad k m / h\), where \(\hat{i}\) points east and \(\hat{\mathbf{j}}\) north. Ship \(B\) is at a distance of 80 \(\mathrm{km}\) east and \(150 \mathrm{~km}\) north of Ship \(A\) and is sailing towards west at \(10 \mathrm{~km} / \mathrm{h}\). A will be at minimum distance from \(B\) in
143747 A girl standing on road holds her umbrella at \(45^{\circ}\) with the vertical to keep the rain away. If she starts running without umbrella with a speed of \(15 \sqrt{2} \mathrm{kmh}^{-1}\), the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is
143749 When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed \(v\), he sees that rain drops are coming at an angle \(60^{\circ}\) from the horizontal. On further increasing the speed of the car to \((1+\beta) \mathrm{v}\), this angle changes to \(45^{\circ}\). The value of \(\beta\) is close to
143750 Ship \(A\) is sailing towards north-east with velocity \(v=30 \hat{i}+50 \hat{j} \quad k m / h\), where \(\hat{i}\) points east and \(\hat{\mathbf{j}}\) north. Ship \(B\) is at a distance of 80 \(\mathrm{km}\) east and \(150 \mathrm{~km}\) north of Ship \(A\) and is sailing towards west at \(10 \mathrm{~km} / \mathrm{h}\). A will be at minimum distance from \(B\) in
143747 A girl standing on road holds her umbrella at \(45^{\circ}\) with the vertical to keep the rain away. If she starts running without umbrella with a speed of \(15 \sqrt{2} \mathrm{kmh}^{-1}\), the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is
143749 When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed \(v\), he sees that rain drops are coming at an angle \(60^{\circ}\) from the horizontal. On further increasing the speed of the car to \((1+\beta) \mathrm{v}\), this angle changes to \(45^{\circ}\). The value of \(\beta\) is close to
143750 Ship \(A\) is sailing towards north-east with velocity \(v=30 \hat{i}+50 \hat{j} \quad k m / h\), where \(\hat{i}\) points east and \(\hat{\mathbf{j}}\) north. Ship \(B\) is at a distance of 80 \(\mathrm{km}\) east and \(150 \mathrm{~km}\) north of Ship \(A\) and is sailing towards west at \(10 \mathrm{~km} / \mathrm{h}\). A will be at minimum distance from \(B\) in
143747 A girl standing on road holds her umbrella at \(45^{\circ}\) with the vertical to keep the rain away. If she starts running without umbrella with a speed of \(15 \sqrt{2} \mathrm{kmh}^{-1}\), the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is
143749 When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed \(v\), he sees that rain drops are coming at an angle \(60^{\circ}\) from the horizontal. On further increasing the speed of the car to \((1+\beta) \mathrm{v}\), this angle changes to \(45^{\circ}\). The value of \(\beta\) is close to
143750 Ship \(A\) is sailing towards north-east with velocity \(v=30 \hat{i}+50 \hat{j} \quad k m / h\), where \(\hat{i}\) points east and \(\hat{\mathbf{j}}\) north. Ship \(B\) is at a distance of 80 \(\mathrm{km}\) east and \(150 \mathrm{~km}\) north of Ship \(A\) and is sailing towards west at \(10 \mathrm{~km} / \mathrm{h}\). A will be at minimum distance from \(B\) in